Games doi: 10.3390/g15020010
Authors: Rim Lahmandi-Ayed Didier Laussel
We study a simple model in which two vertically differentiated firms compete in prices and mass advertising on an initially uninformed market. Consumers differ in their preference for quality. There is an upper bound on prices since consumers cannot spend more on the good than a fixed amount (say, their income). Depending on this income and on the ratio between the advertising cost and quality differential (relative advertising cost), either there is no equilibrium in pure strategies or there exists one of the following three types: (1) an interior equilibrium, where both firms have positive natural markets and charge prices lower than the consumer’s income; (2) a constrained interior equilibrium, where both firms have positive natural markets, and the high-quality firm charges the consumer’s income or (3) a corner equilibrium, where the low-quality firm has no natural market selling only to uninformed customers. We show that no corner equilibrium exists in which the high-quality firm would have a null natural market. At an equilibrium (whenever there exists one), the high-quality firm always advertises more, charges a higher price and makes a higher profit than the low-quality one. As the relative advertising cost goes to infinity, prices become equal and the advertising intensities converge to zero as well as the profits. Finally, the advertising intensities are, at least globally, increasing with the quality differential. Finally, in all cases, as the advertising parameter cost increases unboundedly, both prices converge increasingly towards the consumer’s income.
]]>Games doi: 10.3390/g15020009
Authors: Frago Kourandi Nikolaos Vettas
Here, we study vertical foreclosure in a dynamic setup with learning-by-doing production technologies. There is a downstream monopoly and an upstream duopoly, where manufacturers produce differentiated products and can gain proficiency through the accumulation of their production. We study the dynamic interactions in the vertical chain when the monopolist sets the prices; we find that customer foreclosure may arise in equilibrium when the products are close substitutes and be welfare-enhancing. The rate of learning is lower than the social optimal and a social planner would tend to impose exclusivity more often compared to the downstream monopolist.
]]>Games doi: 10.3390/g15020008
Authors: Daan Lindeman Marius I. Ochea
We investigate the role and performance of imitative behavior in a class of quantity-setting, Cournot games. Within a framework of evolutionary competition between rational, myopic best-response and imitation heuristics with differential heuristics’ costs, we found that the equilibrium stability depends on the sign of the cost differential between the unstable heuristic (Cournot best-response) and the stable one (imitation) and on the intensity of the evolutionary pressure. When this cost differential is positive (i.e., imitation is relatively cheaper vis a vis Cournot), most firms use this heuristic and the Cournot equilibrium is stabilized for market sizes for which it was unstable under Cournot homogeneous learning. However, as the number of firms increases (n=7), instability eventually sets in. When the cost differential is negative (imitation is more expensive than Cournot), complicated quantity fluctuations, along with the co-existence of heuristics, arise already for the triopoly game.
]]>Games doi: 10.3390/g15020007
Authors: Fatima Khanchouche Samir Sbabou Hatem Smaoui Abderrahmane Ziad
In this paper, we examine the class of congestion games with player-specific payoff functions introduced by Milchtaich, I. (1996). Focusing on the special case of two resources, we give a short and simple method for identifying all Nash equilibria in pure strategies. We also provide a computation algorithm based on our theoretical analysis.
]]>Games doi: 10.3390/g15020006
Authors: Alexis Poindron Nizar Allouch
Two groups produce a network good perceived by a third party, such as a police or military institution, as a ‘public bad’, referred to as ‘crime’ for simplicity. These two groups, considered mafias, are assumed to be antagonists, whether they are enemies or competitors in the same market, causing harm to each other’s activities. This paper provides guidelines for the policymaker, typically the police, seeking to minimize overall crime levels by internalizing these negative externalities. One specific question is investigated: the allocation of resources for the police. In general, we recommend a balanced crackdown on both antagonists, but an imbalance in group sizes may lead the police to focus on the more criminal group.
]]>Games doi: 10.3390/g15010005
Authors: Elkhan Richard Sadik-Zada Andrea Gatto Luigi Aldieri Giovanna Bimonte Luigi Senatore Concetto Paolo Vinci
The present investigation elaborates on the level of game theory application for the applied and theoretical analyses of climate change and development studies. This editorial shows that the common good character of global climate alongside the increasing internalization of environmental externalities through national regulations and international environmental treaties jointly result in the increasing congruence between the context of climate change problems and the game theoretical method. Furthermore, the adoption of the Paris Accord by the overwhelming majority of developing countries as well as the disproportionate vulnerability of the Global South have led to an increasing shift in focus with regard to international development cooperation, from poverty alleviation and economic growth to green growth and circular economy solutions, within developing countries. The underutilization of game theory in the context of development studies is not satisfactory. This paper underlines the importance of implementing an impetus to researchers for scholarly discussions and applications of game theory in a discourse on the following topics: 1. economic growth; 2. climate change mitigation and adaptation; and 3. a broader socioeconomic development.
]]>Games doi: 10.3390/g15010004
Authors: Armando Gomes
This paper develops a dynamic model of tender offers in which there is trading on the target’s shares during the takeover, and bidders can freeze out target shareholders (compulsorily acquire remaining shares not tendered at the bid price), features that prevail on almost all takeovers. We show that trading allows for the entry of arbitrageurs with large blocks of shares who can hold out a freezeout—a threat that forces the bidder to offer a high preemptive bid. There is also a positive relationship between the takeover premium and arbitrageurs’ accumulation of shares before the takeover announcement, and the less liquid the target stock, the stronger this relationship is. Moreover, freezeouts eliminate the free-rider problem, but front-end loaded bids, such as two-tiered and partial offers, do not benefit bidders because arbitrageurs can undo any potential benefit and eliminate the coerciveness of these offers. Similarly, the takeover premium is also largely unrelated to the bidder’s ability to dilute the target’s shareholders after the acquisition, also due to potential arbitrage activity.
]]>Games doi: 10.3390/g15010003
Authors: Reza Fallahnejad Mohammad Reza Mozaffari Peter Fernandes Wanke Yong Tan
The Global Malmquist Productivity Index (GMPI) stands as an evolution of the Malmquist Productivity Index (MPI), emphasizing global technology to incorporate all-time versions of Decision-Making Units (DMUs). This paper introduces a novel approach, integrating the Nash Bargaining Game model with GMPI to establish a Cross-Productivity Index. Our primary objective is to develop a comprehensive framework utilizing the Nash Bargaining Game model to derive equitable common weights for different time versions of DMUs. These weights serve as a fundamental component for cross-evaluation based on GMPI, facilitating a holistic assessment of DMU performance over varying time periods. The proposed index is designed with essential properties: feasibility, non-arbitrariness concerning the base time period, technological consistency across periods, and weight uniformity for GMPI calculations between two-time versions of a unit. This research amalgamates cross-evaluation and global technology while employing geometric averages to derive a conclusive cross-productivity index. The core motivation behind this methodology is to establish a reliable and fair means of evaluating DMU performance, integrating insights from Nash Bargaining Game principles and GMPI. This paper elucidates the rationale behind merging the Nash Bargaining Game model with GMPI and outlines the objectives to provide a comprehensive Cross-Productivity Index, aiming to enhance the robustness and reliability of productivity assessments across varied time frames.
]]>Games doi: 10.3390/g15010002
Authors: Mario Blázquez de Paz Nikita Koptyug
We apply three equilibrium selection techniques to study which equilibrium is selected in a hawk–dove game with a multiplicity of equilibria. By using a uniform-price auction as an illustrative example, we find that when the demand in the auction is low or intermediate, the tracing procedure method of Harsanyi and Selten (1988) and the quantal response method of McKelvey and Palfrey (1998) select the same equilibrium. When the demand is high, the tracing procedure method does not select any equilibrium, but the quantal response method still selects the same equilibrium as when the demand is low or intermediate. The robustness to strategic uncertainty method of Andersson, Argenton and Weibull (2014) selects two of the multiple equilibria irrespective of the demand size. We also analyze the impact of an increase in the minimum bid allowed by the auctioneer in the equilibrium selection.
]]>Games doi: 10.3390/g15010001
Authors: Michael S. Harré Husam El-Tarifi
In this article, we investigate the relative performance of artificial neural networks and structural models of decision theory by training 69 artificial intelligence models on a dataset of 7080 human decisions in extensive form games. The objective is to compare the predictive power of AIs that use a representation of another agent’s decision-making process in order to improve their own performance during a strategic interaction. We use human game theory data for training and testing. Our findings hold implications for understanding how AIs can use constrained structural representations of other decision makers, a crucial aspect of our ‘Theory of Mind’. We show that key psychological features, such as the Weber–Fechner law for economics, are evident in our tests, that simple linear models are highly robust, and that being able to switch between different representations of another agent is a very effective strategy. Testing different models of AI-ToM paves the way for the development of learnable abstractions for reasoning about the mental states of ‘self’ and ‘other’, thereby providing further insights for fields such as social robotics, virtual assistants, and autonomous vehicles, and fostering more natural interactions between people and machines.
]]>Games doi: 10.3390/g14060076
Authors: Xinmiao An Yali Dong Xiaomin Wang Boyu Zhang
In this paper, we study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments ei, productivities pi, and rewards ri. In general, this game has a defective Nash equilibrium (NE), in which no one contributes, and multiple cooperative NEs, in which the group’s collective contribution equals the threshold. We then study how multiple dimensions of inequality influence people’s cooperation and coordination. We show that heterogeneity in eipi can promote cooperation in the sense that the existence condition of the defective NE becomes stricter. Furthermore, players with higher eipi are likely to contribute more at a cooperative NE in terms of collective contribution (i.e., absolute contribution multiplied by productivity).
]]>Games doi: 10.3390/g14060075
Authors: Nii-Emil Alexander-Reindorf Paul Cotae
In this paper, we describe the Factored Value MCTS Hybrid Cost-Max-Plus algorithm, a collection of decision-making algorithms (centralized, decentralized, and hybrid) for a multi-agent system in a collaborative setting that considers action costs. Our proposed algorithm is made up of two steps. In the first step, each agent searches for the best individual actions with the lowest cost using the Monte Carlo Tree Search (MCTS) algorithm. Each agent’s most promising activities are chosen and presented to the team. The Hybrid Cost Max-Plus method is utilized for joint action selection in the second step. The Hybrid Cost Max-Plus algorithm improves the well-known centralized and distributed Max-Plus algorithm by incorporating the cost of actions in agent interactions. The Max-Plus algorithm employed the Coordination Graph framework, which exploits agent dependencies to decompose the global payoff function as the sum of local terms. In terms of the number of agents and their interactions, the suggested Factored Value MCTS-Hybrid Cost-Max-Plus method is online, anytime, distributed, and scalable. Our contribution competes with state-of-the-art methodologies and algorithms by leveraging the locality of agent interactions for planning and acting utilizing MCTS and Max-Plus algorithms.
]]>Games doi: 10.3390/g14060074
Authors: Jonathan Merlevede Benjamin Johnson Jens Grossklags Tom Holvoet
In recent years, several high-profile incidents have spurred research into games of timing. A framework emanating from the FlipIt model features two covert agents competing to control a single contested resource. In its basic form, the resource exists forever while generating value at a constant rate. As this research area evolves, attempts to introduce more economically realistic models have led to the application of various forms of economic discounting to the contested resource. This paper investigates the application of a two-parameter economic discounting method, called generalized hyperbolic discounting, and characterizes the game’s Nash equilibrium conditions. We prove that for agents discounting such that accumulated value generated by the resource diverges, equilibrium conditions are identical to those of non-discounting agents. The methodology presented in this paper generalizes the findings of several other studies and may be of independent interest when applying economic discounting to other models.
]]>Games doi: 10.3390/g14060073
Authors: Aaron Foote Maryam Gooyabadi Nikhil Addleman
Poker is a game of skill, much like chess or go, but distinct as an incomplete information game. Substantial work has been done to understand human play in poker, as well as the optimal strategies in poker. Evolutionary game theory provides another avenue to study poker by considering overarching strategies, namely rational and random play. In this work, a population of poker playing agents is instantiated to play the preflop portion of Texas Hold’em poker, with learning and strategy revision occurring over the course of the simulation. This paper aims to investigate the influence of learning dynamics on dominant strategies in poker, an area that has yet to be investigated. Our findings show that rational play emerges as the dominant strategy when loss aversion is included in the learning model, not when winning and magnitude of win are of the only considerations. The implications of our findings extend to the modeling of sub-optimal human poker play and the development of optimal poker agents.
]]>Games doi: 10.3390/g14060072
Authors: Kalliopi Kastampolidou Theodore Andronikos
This paper introduces a new quantum game called Quantum Tapsilou that is inspired by the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the most important characteristic of the traditional game. In the classical game, both players have 14 probability to win. The quantum version retains this characteristic feature, which is that both players have the same probability to win, but only now this probability varies considerably and depends on previous moves and choices. The two most important novelties of Quantum Tapsilou can be attributed to its implementation of entanglement via the use of rotation gates instead of Hadamard gates, which generates Bell-like states with unequal probability amplitudes, and the integral use of groups. In Quantum Tapsilou both players agree on a specific cyclic rotation group of order n, for some sufficiently large n. The game is based on the chosen group, in the sense that both players will draw their moves from its elements. More specifically, both players will pick rotations from this group to realize their actions using the corresponding Ry rotation gates. In the Quantum Tapsilou game, it is equally probable for both players to win. This fact is in accordance with a previous result in the literature showing that quantum games where both players choose their actions from the same group, exhibit perfect symmetry by providing each player with the possibility to pick the move that counteracts the other player’s action.
]]>Games doi: 10.3390/g14060071
Authors: Saori Chiba Kaiwen Leong
In this paper, we investigate optimal delegation mechanisms in the presence of countervailing conflicts of interest in the context of principal–agent problems. We introduce two dimensions of conflict of interest—pandering incentives related to the outside option and project biases. We compare three delegation mechanisms: full delegation, veto-based delegation, and communication (no delegation). Contrary to conventional one-dimensional conflict models, our findings reveal a non-monotonic relationship between pandering incentives and bias. These conflicts counterbalance each other, resulting in a principal’s benefit from delegation not strictly decreasing with increased bias. Surprisingly, delegation to a biased agent can be advantageous in certain scenarios. This research sheds light on the complex dynamics of delegation mechanisms when confronted with countervailing conflicts of interest, offering insights into decision-making in principal–agent relationships.
]]>Games doi: 10.3390/g14060070
Authors: Stefano Colombo Arijit Mukherjee
We analyze the location of final goods producers under spatial competition with strategic input price determination by firm-specific input suppliers when the final goods producers undertake complete outsourcing or bi-sourcing. Under complete outsourcing, the final goods producers locate closer as the distance between the input suppliers decreases, but the distance between the final goods producers may increase or decrease with the transportation costs of the consumers and the transportation costs between the input suppliers and the final goods producers depending on the distance between the input suppliers. The possibility of bi-sourcing reduces the benefit from saving the transportation costs between the input suppliers and the final goods producers, and creates effects which are opposite to those under complete outsourcing. Thus, our results differ significantly from the extant literature considering either no strategic input price determination or strategic input price determination under competition in the input market. We also discuss the implications on the profits, consumer surplus and welfare, and the implications of endogenous location choice of the input suppliers.
]]>Games doi: 10.3390/g14060069
Authors: Jaesoo Kim Dongsoo Shin
In an agency model with adverse selection, we study how hidden interactions between agents affect the optimal contract. The principal employs two agents who learn their task environments through their involvement. The principal cannot observe the task environments. It is important to note that hidden interactions, such as acts of sabotage or help between the agents, have the potential to alter each other’s task environments. Our analysis encompasses two distinct organizational structures: competition and cooperation. Without hidden interactions, the competitive structure is optimal because the cooperative structure only provides the agents with more flexibility to collusively misrepresent their task environments. With hidden interactions, however, the cooperative structure induces the agents to help each other to improve the task environments while removing sabotaging incentives at no cost once collusion is deterred. As a result, the cooperative structure can be optimal in such a case. We discuss the link between production technology and organizational structure, finding that complementarity in production favors cooperative structures.
]]>Games doi: 10.3390/g14060068
Authors: Mario Lefebvre
A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk {Xn,n=0,1,…} in the continuation region C:={1,2,…}, and the second player seeks to maximize the survival time in C. The process starts at X0=x>0 and the game ends the first time Xn≤0. An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly.
]]>Games doi: 10.3390/g14060067
Authors: Akio Matsumoto Ferenc Szidarovszky Maryam Hamidi
The asymptotical properties of a special dynamic two-person game are examined under best-response dynamics in both discrete and continuos time scales. The direction of strategy changes by the players depend on the best responses to the strategies of the competitors and on their own strategies. Conditions are given first for the local asymptotical stability of the equilibrium if instantaneous data are available to the players concerning all current strategies. Next, it is assumed that only delayed information is available about one or more strategies. In the discrete case, the presence of delays has an effect on only the order of the governing difference equations. Under continuous scales, several possibilities are considered: each player has a delay in the strategy of its competitor; player 1 has identical delays in both strategies; the players have identical delays in their own strategies; player 1 has different delays in both strategies; and the players have different delays in their own strategies. In all cases, it is assumed that the equilibrium is asymptotically stable without delays, and we examine how delays can make the equilibrium unstable. For small delays, the stability is preserved. In the cases of one-delay models, the critical value of the delay is determined when stability changes to instability. In the cases of two and three delays, the stability-switching curves are determined in the two-dimensional space of the delays, where stability becomes lost if the delay pair crosses this curve. The methodology is different for the one-, two-, and three-delay cases outlined in this paper.
]]>Games doi: 10.3390/g14050066
Authors: Amitrajeet A. Batabyal Hamid Beladi
We exploit the public good attributes of Ganges water pollution cleanup and theoretically analyze an aggregate economy of two cities—Kanpur and Varanasi—through which the Ganges flows. Our specific objective is to study whether water pollution cleanup in these two cities ought to be provided in a centralized or in a decentralized manner. We first determine the efficient cleanup amounts that maximize the aggregate surplus from making the Ganges cleaner in the two cities. Second, we compute the optimal amount of water pollution cleanup in the two cities in a decentralized regime in which spending on cleanup is financed by a uniform tax on the city residents. Third, we ascertain the optimal amount of water pollution cleanup in the two cities in a centralized regime subject to equal provision of cleanup and cost sharing. Fourth, we show that if the two cities have the same preference for pollution cleanup, then centralization is preferable to decentralization as long as there is a spillover from pollution cleanup. Finally, we show that if the two cities have dissimilar preferences for pollution cleanup, then centralization is preferable to decentralization as long as the spillover exceeds a certain threshold.
]]>Games doi: 10.3390/g14050065
Authors: Werner Güth Hironori Otsubo
Institutions may rely on fundamental principles, e.g., of legal philosophy, but may also have evolved according to institutional fitness, as gauged by a society’s well-being. In our stylized framework where two fundamental principles, equality and efficiency, conflict with each other, one of the three players is the third party who faces two symmetric co-players as culprits and determines whether to sanction the two culprits discriminatorily or treat them with parity. Relying on the theory of equilibrium selection, we derived equilibrium solutions and experimentally tested our behavioral hypotheses. We found that asymmetry in wealth between the two culprits let the sanctioning agent hold the richer culprit more responsible. Furthermore, our results demonstrated that when the sanctioning agent’s decision was observable, sanctioning the two culprits discriminatorily induced them to coordinate on an efficient outcome.
]]>Games doi: 10.3390/g14050064
Authors: Robert P. Gilles Lina Mallozzi
We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players—constituting a hierarchical network. The power distribution embedded within a hierarchical network can be represented through appropriate TU-games. We investigate the properties of these TU-representations and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a core power gauge, investigate the relationship of the Gately with the β-measure, and construct an axiomatisation of the Gately measure.
]]>Games doi: 10.3390/g14050063
Authors: Stewart Ethier Jiyeon Lee
In a previous paper, we considered several models of the parlor game baccara chemin de fer, including Model B2 (a 2×2484 matrix game) and Model B3 (a 25×2484 matrix game), both of which depend on a positive-integer parameter d, the number of decks. The key to solving the game under Model B2 was what we called Foster’s algorithm, which applies to additive 2×2n matrix games. Here “additive” means that the payoffs are additive in the n binary choices that comprise a player II pure strategy. In the present paper, we consider analogous models of the casino game baccara chemin de fer that take into account the 100α percent commission on Banker (player II) wins, where 0≤α≤1/10. Thus, the game now depends not just on the discrete parameter d but also on a continuous parameter α. Moreover, the game is no longer zero sum. To find all Nash equilibria under Model B2, we generalize Foster’s algorithm to additive 2×2n bimatrix games. We find that, with rare exceptions, the Nash equilibrium is unique. We also obtain a Nash equilibrium under Model B3, based on Model B2 results, but here we are unable to prove uniqueness.
]]>Games doi: 10.3390/g14050062
Authors: Athanasios Kehagias
We formulate and study a two-player duel game as a terminal payoffs stochastic game. Players P1,P2 are standing in place and, in every turn, each may shoot at the other (in other words, abstention is allowed). If Pn shoots Pm (m≠n), either they hit and kill them (with probability pn) or they miss and Pm is unaffected (with probability 1−pn). The process continues until at least one player dies; if no player ever dies, the game lasts an infinite number of turns. Each player receives a positive payoff upon killing their opponent and a negative payoff upon being killed. We show that the unique stationary equilibrium is for both players to always shoot at each other. In addition, we show that the game also possesses “cooperative” (i.e., non-shooting) non-stationary equilibria. We also discuss a certain similarity that the duel has to the iterated Prisoner’s Dilemma.
]]>Games doi: 10.3390/g14050061
Authors: Mevan Wijewardena Michael J. Neely
This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an ϵ-approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique.
]]>Games doi: 10.3390/g14050060
Authors: Jijian Fan
We examine a bargaining game in which players cannot make arbitrary offers. Instead, players alternately decide whether to accept or delay, and are rewarded with an indivisible portion and a perishable transfer that depends on the round. Our analysis demonstrates that when the initial transfer is large enough, the subgame perfect Nash equilibrium consists of a finite number of rounds of delay before an agreement is reached. The equilibrium delay is longer when the players are more patient, and when the transfer is initially higher and depreciates slower. Nevertheless, the game’s chaotic characteristic makes it arduous to forecast the exact number of delayed rounds or which player will make the ultimate decision. This game can be applied to many social scenarios, particularly those with exogenous costs.
]]>Games doi: 10.3390/g14050059
Authors: Sebastian Cano-Berlanga María-José Solís-Baltodano Cori Vilella
Water scarcity is a growing problem in many regions worldwide. According to the United Nations, around one-fifth of the world’s population lives in areas where water is scarce. Another one-quarter of the world’s population has to face water supply cuts, mainly because this proportion of the population lacks the necessary infrastructure to acquire water from rivers and aquifers (UN, 2005). Water is a resource that is essential to human survival and is also present in all productive processes in the economy. Therefore, we are challenged to adequately manage water to ensure the population’s well-being and to achieve socioeconomic development. Specifically, this paper analyzes the situation present in the summer of 2022 at Riudecanyes (a village in Catalonia, Spain), where a drought problem exists. We propose applying the conflicting claims problem theory to give possible solutions to distribute the water. We propose to use this theory to describe the distribution of the available irrigation hours in 2022, considering the demand made by the farmers in the previous year, when there was regular irrigation.
]]>Games doi: 10.3390/g14050058
Authors: Julide Yazar Robert J. Gitter
We consider a game-theoretic model of undocumented immigration with the aim of emphasizing the strategic interaction between the different forces affecting the issue. Specifically, we analyze the strategic interaction between firms in the destination country, native labor, the elected officials in the destination country, and the undocumented immigrants from the Source Country. We show that the impact of border enforcement is dampened because strategic interaction between the players will tend to mute any unilateral changes. We also study the effect of uncertainty in the labor market on migration issues and analyze the two cases where policymakers have to make their decisions before (ex-ante) or after (ex-post) the market state is realized.
]]>Games doi: 10.3390/g14040056
Authors: Amit Gayer
This research paper investigates a duopolistic market characterized by vertical product differentiation. The study considers both product qualities and consumer preferences represented as one-dimensional intervals. The focus is on analyzing the equilibrium in a duopoly game with convex production costs. In this setting, each firm has the option to present a multi-product strategy consisting of quality–price pairs, and their profits are determined by the decisions made by consumers. The findings of the study reveal that, under typical consumer preference conditions, both firms tend to offer a single quality–price pair. Additionally, the market is shown to be fully served, and firm profits decrease as the index of product quality increases. A comparative analysis is also conducted with the case of a monopoly.
]]>Games doi: 10.3390/g14040057
Authors: Mishal Assif William Kennedy Iraj Saniee
In this paper, we address the problem of fair sharing of the total value of a crowd-sourced network system between major participants (founders) and minor participants (crowd) using cooperative game theory. We use the framework of a Shapley allocation which is regarded as a fundamental method of computing the fair share of all participants in a cooperative game when the values of all possible coalitions could be quantified. To quantify the value of all coalitions, we define a class of value functions for crowd-sourced systems which capture the contributions of the founders and the crowd plausibly and derive closed-form expressions for Shapley allocations to both. These value functions are defined for different scenarios, such as the presence of oligopolies or geographic spread of the crowd, taking network effects, including Metcalfe’s law, into account. A key result we obtain is that under quite general conditions, the crowd participants are collectively owed a share between 12 and 23 of the total value of the crowd-sourced system. We close with an empirical analysis demonstrating the consistency of our results with the compensation offered to the crowd participants in some public internet content sharing companies.
]]>Games doi: 10.3390/g14040055
Authors: Sung-Hoon Park Chad E. Settle
We investigate the impact of observability of contracts between a plaintiff and his attorney on both the efficiency of the environmental conflict and the fairness of the resulting outcome from the environmental conflict. By including two specific game-theoretic models (an observable-contract game and an unobservable-contract game), we find two key results: (i) The unobservability of a contract may increase inefficiency of the environmental conflict in terms of legal efforts; however, (ii) the unobservability of a contract may increase the fairness of the outcome in terms of the plaintiff’s probability of winning the contest.
]]>Games doi: 10.3390/g14040054
Authors: Harold Houba Françeska Tomori
Market power in water markets can be modeled as simultaneous quantity competition on a river structure and analyzed by applying social equilibrium. In an example of a duopoly water market, we argue that the lack of backward induction logic implies that the upstream supplier foregoes profitable strategic manipulation of water to the downstream supplier. To incorporate backward induction, we propose the Stackelberg social equilibrium concept. We prove the existence of Stackelberg social equilibrium in duopoly water markets with an upstream–downstream river structure and derive it in the example of a duopoly market.
]]>Games doi: 10.3390/g14040053
Authors: Debasmita Basak
We consider a vertically related market where one quantity-setting and another price-setting downstream firm negotiate the terms of a two-part tariff contract with an upstream input supplier. In contrast to the traditional belief, we show that the price-setting firm produces a higher output and earns a higher profit than the quantity-setting firm when bargaining is decentralised. Additionally, both firms produce the same output, whereas the profit is higher under the price-setting firm than the quantity-setting firm when bargaining is centralised.
]]>Games doi: 10.3390/g14040052
Authors: Gafurjan Ibragimov Marks Ruziboev Ibroximjon Zaynabiddinov Bruno Antonio Pansera
We investigate a differential evasion game with multiple pursuers and an evader for the infinite systems of differential equations in ℓ2. The control functions of the players are subject to geometric constraints. The pursuers’ goal is to bring the state of at least one of the controlled systems to the origin of ℓ2, while the evader’s goal is to prevent this from happening in a finite interval of time. We derive a sufficient condition for evasion from any initial state and construct an evasion strategy for the evader.
]]>Games doi: 10.3390/g14040051
Authors: Yu-Hsien Liao
By considering the maximal efficacy among allocation vectors, we define two power indices under specific multicriteria conditions. Additionally, we introduce a reduction approach to the axiomatic framework for these power indices. Furthermore, we propose an alternative formulation that focuses on discrepancy mapping. Based on reduction and discrepancy mapping, we also provide two dynamic procedures.
]]>Games doi: 10.3390/g14030050
Authors: Shinichi Ishihara Junnosuke Shino
Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval instead of a real number. This study revisits two interval game versions of Shapley values (i.e., the interval Shapley value and the interval Shapley-like value) and characterizes them using an axiomatic approach. For the interval Shapley value, we show that the existing axiomatization can be generalized to a wider subclass of interval games called size monotonic games. For the interval Shapley-like value, we show that a standard axiomatization using Young’s strong monotonicity holds on the whole class of interval games.
]]>Games doi: 10.3390/g14030049
Authors: Luís Pacheco Júlio Lobão Sílvia Coelho
The theoretical literature on risk aversion and Expected Utility Theory is extensive; however, the analysis of this behaviour with natural experiments could be more comprehensive. In this paper, we use data from 120 episodes of the Portuguese version of the TV game show The Price is Right, namely from The Wheel game, to explore risk aversion as well as the impact of gender in decision-making. The Wheel game has straightforward rules and huge expected payoffs. All contestants have access to the same information and distributions of uncertainty, making it a unique field laboratory to conduct an experimental test of rational decision theory. The objective is to infer the risk aversion levels of decision-makers from their choice to turn the wheel and the influence of gender on risk attitudes. There is a widespread view that women are more risk-averse than men. However, we could not reject the hypothesis that women and men have the same level of risk aversion. Nevertheless, we have evidence that contestants are more risk-averse than risk-seeking. The omission bias, loss aversion and regret can explain that behaviour.
]]>Games doi: 10.3390/g14030048
Authors: Scott M. Gilpatric Ye Hong
We consider the design of a contest in which the prize may motivate not only productive efforts, but also some damaging aggressive behavior by contestants. The organizer must choose prizes and an enforcement regime defined as a limit on how much aggressiveness will be tolerated and the probability of inspection. When the value of contestants’ output is low, it may be optimal to motivate much less effort than first best because the prize spread necessary to induce higher effort necessitates a high level of enforcement, which is not worth the cost. On the other hand, when the output value is sufficiently high, it becomes optimal to offer a high prize spread to motivate substantial but still below first-best effort, with costly enforcement then being employed to constrain damaging aggressive behavior. Additionally, a less accurate inspection technology is associated with a tighter limit on aggressive behavior, and “zero tolerance” can be optimal if the aggressive behavior has no value.
]]>Games doi: 10.3390/g14030047
Authors: Chirantan Ganguly Indrajit Ray
In the Crawford–Sobel (uniform, quadratic utility) cheap-talk model, we consider a simple mediation scheme (a communication device) in which the informed agent reports one of the N possible elements of a partition to the mediator and then the mediator suggests one of the N actions to the uninformed decision-maker according to the probability distribution of the device. We show that no such simple mediated equilibrium can improve upon the unmediated N-partition Crawford–Sobel equilibrium when the preference divergence parameter (bias) is small.
]]>Games doi: 10.3390/g14030046
Authors: Manela Karunadasa Katri K. Sieberg Toni Tapani Kristian Jantunen
This experiment examines the relationship between payment systems and the quality and quantity of services provided in credence goods markets. By using a real-effort task to stimulate the decision making of service providers, the study finds that payment systems do indeed have an impact on service provision. Specifically, providers in fee-for-service systems over-provide, while those in salary systems under-provide services. Additionally, there is a lack of alignment between the services provided under fee-for-service and the actual needs of customers, resulting in a substantial loss of customer benefits under fee-for-service in comparison to under salary. The study also finds that providers in fee-for-service systems perform more faulty tasks than those in salary, indicating that they may prioritize quantity over quality in their services. As for insurance, the results of this study show no significant effect of insurance on the number of services provided; however, customers without insurance received significantly more faulty tasks. Based on these results, the study concludes that payment systems play an important role in determining the quality and quantity of services provided in credence goods markets. Overall, this study highlights the need for a better alignment between customer needs and services provided under fee-for-service systems.
]]>Games doi: 10.3390/g14030045
Authors: William C. Grant
In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players.
]]>Games doi: 10.3390/g14030044
Authors: Tobias Hiller
Training in firms has an effect on the productivity of employees who receive the training, and depending on the production technology, on the other employees as well. Meanwhile, changing the remuneration structure within a team can change the stability of a team. In this paper, we apply the production games approach of cooperative game theory to analyze how training employees affects the stability of team structures and employee wages. Concretely, we apply coalition structures and the χ value. Our results are in line with the literature and numerous further research questions can be addressed based on our approach.
]]>Games doi: 10.3390/g14030043
Authors: Zhongwen Chen Xiaojian Zhao
This paper theoretically studies the interaction between an informed borrower and an uninformed lender facing possible default of a loan application. The lender is motivated to invest cognitive resources before making a lending decision. If the regulatory fine is weak, it is impossible for a bad-debt borrower to fully disclose his situation in the application. In this case, when the likelihood of a bad debt is low, the borrower always claims that nothing in the application is wrong. Otherwise, the borrower randomizes between full disclosure and information suppression. The transaction cost of the lender’s pre-lending cognition increases with the default probability, as the default probability is small and decreases thereafter. Evidence from a peer-to-peer lending platform with 816,274 observations between 2012 and 2015 in the United States is largely consistent with our model implications.
]]>Games doi: 10.3390/g14030042
Authors: Alessandra F. Lütz Marco Antonio Amaral Ian Braga Lucas Wardil
The stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already well established and stable due to sanctions imposed on non-conforming members. Thus, how does a population shift from the current social contract to a better one? In other words, how can a social system leave a locally optimum configuration to achieve a globally optimum state? Here, we investigate the effect of promoting diversity on the evolution of social contracts. We consider group-structured populations where individuals play the stag-hunt game in all groups. We model the diversity incentive as a snowdrift game played in a single focus group where the individual is more prone to adopting a deviant norm. We show that a moderate diversity incentive is sufficient to change the system dynamics, driving the population over the stag-hunt invasion barrier that prevents the global optimum being reached. Thus, an initial fraction of adopters of the new, better norm can drive the system toward the optimum social contract. If the diversity incentive is not too large, the better social contract is the new equilibrium and remains stable even if the incentive is turned off. However, if the incentive is large, the population is trapped in a mixed equilibrium and the better social norm can only be reached if the incentive is turned off after the equilibrium is reached. The results are obtained using Monte Carlo simulations and analytical approximation methods.
]]>Games doi: 10.3390/g14030041
Authors: Xu Chen Xuan Di Zechu Li
Autonomous driving (AV) technology has elicited discussion on social dilemmas where trade-offs between individual preferences, social norms, and collective interests may impact road safety and efficiency. In this study, we aim to identify whether social dilemmas exist in AVs’ sequential decision making, which we call “sequential driving dilemmas” (SDDs). Identifying SDDs in traffic scenarios can help policymakers and AV manufacturers better understand under what circumstances SDDs arise and how to design rewards that incentivize AVs to avoid SDDs, ultimately benefiting society as a whole. To achieve this, we leverage a social learning framework, where AVs learn through interactions with random opponents, to analyze their policy learning when facing SDDs. We conduct numerical experiments on two fundamental traffic scenarios: an unsignalized intersection and a highway. We find that SDDs exist for AVs at intersections, but not on highways.
]]>Games doi: 10.3390/g14030040
Authors: David B. Johnson Jonathan Rogers
When there is direct competition for a position of power (promotion, elected office, etc.), competitors are tempted to cheat to increase their chances of winning. If they do so successfully, then how they rationalize their cheating can determine how they treat the losers of the competition. In this paper, we explore how the winners of a promotion tournament treat the losers, using a two stage laboratory experiment run in Canada and the United Arab Emirates. In the first stage, subjects compete to earn the role of the dictator in a dictator game, which takes place in the second stage. We vary whether or not subjects can cheat during the competition. The results of the experiment can be summarized as follows: (1) cheating significantly increases altruism in some tournament winners, (2) winners who cheat the most are significantly less altruistic than winners who cheated only a little, (3) there are significant differences in cheating behavior across the two populations, and (4) cheating behavior can be at least partially attributed to differences in intelligence and beliefs across the two populations.
]]>Games doi: 10.3390/g14030039
Authors: Adam Meirowitz
We point out an equivalence between a class of games in which players negotiate while fighting and a class of games in which a buyer and seller negotiate over terms. Importantly and perhaps ironically, bargaining before fighting is strategically distinct from bargaining before a change of ownership but bargaining while fighting is equivalent to bargaining before a change of ownership. These connections and intuition from models of bilateral trade help shed light on two mechanisms for learning while frighting: inference based on observing strategic choices and information leakage on the battlefield. Debates on the relative importance of these to mechanism are addressed; some subtle clarifications to extant arguments are provided. Moreover, the importance of learning hard information from the battlefield is connected to work on Coasian Dynamics with information leakage and avenuse for future work relying on advances in behavioral theory are sketched out.
]]>Games doi: 10.3390/g14030038
Authors: Manuel A. Utset
The paper studies bargaining games involving players with present-biased preferences. The paper shows that the relative timing of bargaining rewards and bargaining costs will determine whether the players’ present-bias will affect bargaining outcomes. In cases where players agree to a bargain in period 1 and experience all bargaining payoffs in period 2, the players will act in a time-consistent fashion. When time-inconsistent players incur immediate bargaining costs to produce delayed rewards, they will have an incentive to procrastinate. On the other hand, when players receive immediate bargaining rewards and incur delayed costs, they will have incentives to agree to bargains too soon and to agree to inefficient bargains. The paper shows that the players’ awareness of their own and the other player’s present-biased preferences will determine whether they engage in repeated time-inconsistent bargaining. A naïve player who engages in time-inconsistent bargaining will suffer welfare losses. We show that time-inconsistent bargaining can also create spillover welfare losses for other players. A time-consistent player who is counterparty-naïve about the other player can suffer spillover welfare losses that can be higher than those incurred by the time-inconsistent player. As a result, counterparty-sophisticated players will have an incentive to use cross-commitment devices to reduce the likelihood of spillover welfare losses. The paper also shows that cross commitment devices that target immediate payoffs dominate cross-commitments that target delayed payoffs. Finally, the paper shows that time-inconsistent bargaining can lead to inefficient delays in agreeing to bargains and in exiting bargaining relationships.
]]>Games doi: 10.3390/g14030037
Authors: Charlotte Roman Paolo Turrini
In transportation networks, incomplete information is ubiquitous, and users often delegate their route choice to distributed route planners. To model and study these systems, we introduce network control games, consisting of multiple actors seeking to optimise the social welfare of their assigned subpopulations through resource allocation in an underlying nonatomic congestion game. We first analyse the inefficiency of the routing equilibria by calculating the Price of Anarchy for polynomial cost functions, and then, using an Asynchronous Advantage Actor–Critic algorithm implementation, we show that reinforcement learning agents are vulnerable to choosing suboptimal routing as predicted by the theory. Finally, we extend the analysis to allow vehicles to choose their route planner and study the associated equilibria. Our results can be applied to mitigate inefficiency issues arising in large transport networks with route controlled autonomous vehicles.
]]>Games doi: 10.3390/g14030036
Authors: Sabrina Evans Paolo Turrini
We study the strategic similarity of game positions in two-player extensive games of perfect information by looking at the structure of their local game trees, with the aim of improving the performance of game-playing agents in detecting forcing continuations. We present a range of measures over the induced game trees and compare them against benchmark problems in chess, observing a promising level of accuracy in matching up trap states. Our results can be applied to chess-like interactions where forcing moves play a role, such as those arising in bargaining and negotiation.
]]>Games doi: 10.3390/g14030035
Authors: Francesca Flamini
We analyze a dynamic bargaining game where parties can agree to implement a policy change, which is costly (beneficial) in the short-run but beneficial (costly) in the long-run. When the status-quo is endogenized (at least in some components), we show that the more farsighted party can induce their rival to accept the short-run costs of policy changes designed to generate benefits in the long-run. This is more common when players’ asymmetries are less pronounced, the status-quo is fully endogenized and the state depreciates more quickly.
]]>Games doi: 10.3390/g14030034
Authors: Yannick Gabuthy
A smart contract can be defined as a computer program, stored on a blockchain, which allows a transaction or an agreement—defined ex-ante—to be self-executed when some conditions are met, and without the need for a central authority to enforce it. Even if this new technology is very promising, it may face a challenge: the codified nature of smart contracts creates new types of disputes that require new mechanisms of dispute resolution, which are precisely based on the blockchain. The aim of this article is to analyze one of these emerging mechanisms, namely Kleros, which is a blockchain-based dispute resolution platform implying crowdsourced jurors whose incentives to make fair decisions are based on game theory. The Kleros case provides also a basis for a broader discussion on the future of the decentralized justice market.
]]>Games doi: 10.3390/g14020033
Authors: Andrea Caravaggio Luigi De Cesare Andrea Di Liddo
This article studies a leader–follower differential game with a finite horizon, where a single buyer reacts to the selling price set by an agency (water supplier). The Open-Loop Stackelberg equilibrium is calculated, assuming that the user demand is fully satisfied (that is, the interior solution is considered), and the following different tariff schemes are analyzed: linear scheme, increasing block tariff, and convex tariff. Numerical simulations highlight how tariff convexity and seasonality in buyer’s preferences affect water price and demand, and the dynamics of the basin over time. The study shows that synchrony or asynchrony between basin recharge and buyer cyclical demand can dramatically affect the dynamics and basin levels observed at the end of the time period considered. Additionally, the presence of a large number of fluctuations in buyer preferences affects basin fluctuations, while natural recharge may help in maintaining acceptable levels of future water demands.
]]>Games doi: 10.3390/g14020032
Authors: Tobias Hiller
Electoral thresholds in the context of parliamentary elections are an instrument for preventing the fragmentation of parliaments and facilitate the formation of a coalition government. However, the clauses also introduce distortions and modify the equality of electoral votes in an election. In order to decide to what extent these negative effects can be accepted, it is necessary to measure the difficulties in forming a coalition government and to quantify the effects of electoral thresholds on these difficulties. For this issue, we introduce a concept based on cooperative game theory which takes into account the distribution of seats in parliament and coalition statements of parties.
]]>Games doi: 10.3390/g14020031
Authors: Chen Cohen Roy Darioshi Shmuel Nitzan
This article presents an equivalence theorem in the context of Tullock’s augmented lottery contest with external or internal cost reimbursement. Three alternative modes of reimbursement are studied. The equivalence implies that, even though the augmented contest is vulnerable to framing biases, it is strategically neutral.
]]>Games doi: 10.3390/g14020030
Authors: Luyao Niu Bhaskar Ramasubramanian Andrew Clark Radha Poovendran
This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that operate in adversarial environments have typically been abstracted as stochastic games (SGs); however, because traditional SG models do not incorporate a notion of time, they cannot be used in a setting where the objective is time-sensitive. To address this, we introduce durational stochastic games (DSGs). DSGs generalize SGs to incorporate a notion of time and model the adversary’s abilities to tamper with the control input (actuator attack) and manipulate the timing information that is perceived by the CPS (timing attack). We define notions of spatial, temporal, and spatio-temporal robustness to quantify the amounts by which system trajectories under the synthesized policy can be perturbed in space and time without affecting satisfaction of the MITL objective. In the case of an actuator attack, we design computational procedures to synthesize controllers that will satisfy the MITL task along with a guarantee of its robustness. In the presence of a timing attack, we relax the robustness constraint to develop a value iteration-based procedure to compute the CPS policy as a finite-state controller to maximize the probability of satisfying the MITL task. A numerical evaluation of our approach is presented on a signalized traffic network to illustrate our results.
]]>Games doi: 10.3390/g14020029
Authors: Jen-Yao Lee Chen-Chia Fan Chien-Shu Tsai
This paper considers the collusive stability of downstream competition in a vertical market with network externalities and cost asymmetry. A dynamic collusion game is constructed, and backward induction is employed to solve the subgame perfect Nash equilibrium. We show that larger network externalities lead to less collusive incentive for an inefficient firm, while for an efficient firm, this depends on the efficiency gap. An increase in network externalities will destabilize the downstream collusion when the cost asymmetry is large and network externalities are relatively weak.
]]>Games doi: 10.3390/g14020028
Authors: Frank Krueger
Trust and reciprocity are fundamental for the cohesion and stability of human society, as they are essential components of cooperative exchange [...]
]]>Games doi: 10.3390/g14020027
Authors: Theofanis Tsoulouhas
The theory of relative performance evaluation has come a long way since its inception, so much so that it is now a major research branch in economic theory [...]
]]>Games doi: 10.3390/g14020026
Authors: Naoto Aoyama Emilson Caputo Delfino Silva
Under the ‘new normal’ in the labor market, individuals can work remotely or in person, a hybrid work mode that became ubiquitous during the pandemic. This paper studies the efficiency of decentralized leadership in federations in which hybrid work is the modus operandi. Self-interested regional governments and a benevolent central government interact strategically in dynamic games in which there are provisions of federal and regional public goods and interregional income and fiscal transfers, the population is attached to regions and hybrid work creates a common labor market in the federation. In this setting, we first show that decentralized leadership is inefficient if the center controls income transfers only. This result provides an efficiency enhancing motivation for the center to additionally control earmarked transfers: we demonstrate that decentralized leadership is efficient whenever the center controls both income and earmarked transfers. However, this is not the only federal regime in which decentralized leadership is efficient. It is efficient in the absence of earmarked transfers if it is appropriately selective: when the regional governments commit to the provision of the federal public only and the center redistributes income across regions.
]]>Games doi: 10.3390/g14020025
Authors: Armando José Garcia Pires
In this paper, we look at two research questions. First, can lower ad-valorem taxes, on the selling of news and on the selling of advertising, conduce to lower prices in the media sector? Second, can lower ad-valorem taxes stimulate firms to increase the diversity of content that they offer? The purpose of this work is to give tax political guidelines to policy makers for the media sector. This is important for a sector that has seen the reduction in payment subscriptions by readers (due to competition from free news from the Internet), and reduction of advertisement revenues due to competition from media giants like Google and Facebook. With this purpose we build on the Hoteling product competition model, which is the workhorse model in media economics. We show that ad-valorem taxes on the selling of advertising are preferable to ad-valorem taxes on the selling of news because the former conduce to reduction in prices of newspaper. However, both ad-valorem taxes on the selling of news and on the selling of advertisement reduces media diversity, because they reduce revenues that media firms can use to invest in media content.
]]>Games doi: 10.3390/g14020024
Authors: Stanislav Stoykov Ivan Kostov
A numerical procedure capable of obtaining the equilibrium states of oligopoly markets under several assumptions is presented. Horizontal and vertical product differentiation were included by taking into account Euclidean distance in a two-dimensional space and quality characteristics of the product. Different quality preferences of consumers were included in the model. Firms implement two strategies in the market: profit maximization and market share maximization. Numerical discretization of a two-dimensional area was performed for computing the equilibrium prices which allows one to consider any market area and any location of the firms. Four scenarios of oligopoly markets were developed by combining both strategies from one side and competitive behavior and a partial cartel agreement from another side. The main differences between the scenarios are outlined. Profits, market shares and equilibrium prices are presented and compared. The influence of collusion, the existence of participants with a market share maximization strategy and consumer preferences on the firm’s profits and equilibrium prices were examined. Cases whereby firms prefer to leave the cartel were investigated. Best locations for the setting of a new store for profit maximization are shown and discussed.
]]>Games doi: 10.3390/g14020023
Authors: Heinrich H. Nax
How humans behave in repeated strategic interactions, how they learn, how their decisions adapt, and how their decision-making evolves is a topic of fundamental interest in behavioral economics and behavioral game theory [...]
]]>Games doi: 10.3390/g14020022
Authors: Xinrong Yang Zhenping Geng Haitao Li
In this paper, a detailed survey is presented for the analysis and control of networked evolutionary games via the matrix method. The algebraic form of networked evolutionary games is firstly recalled. Then, some existing results on networked evolutionary games are summarized. Furthermore, several generalized forms of networked evolutionary games are reviewed, including networked evolutionary games with time delay, networked evolutionary games with bankruptcy mechanism, networked evolutionary games with time-varying networks, and random evolutionary Boolean games. The computational complexity of general networked evolutionary games is still challenging, which limits the application of the matrix method to large-scale networked evolutionary games. Future works are finally presented in the conclusion.
]]>Games doi: 10.3390/g14020021
Authors: Davood Bayat Hadi Mohamadpour Huihua Fang Pengfei Xu Frank Krueger
Trust and reciprocity have paramount importance in cooperative relationships. The influence of psychological effects such as framing and anchoring on trust and reciprocity has been investigated; however, the impact of an order effect on them is still unexplored. The goal of our study was to examine how order impacts the framing of trust and reciprocity by manipulating framing and order as within- and between-subjects factors, respectively. Different groups of participants first completed two framings of the one-shot trust game (give vs. take frame) in a counterbalanced order (give first and then take second vs. take first then give second) in the role of trustors or trustees and rated the expectations of their counterparts’ decisions afterward. Our results revealed higher trust in the take than give frame in the first decision and a reverse outcome in the second decision due to strong anchoring. Reciprocity was higher in the give than take frame in the first decisions, and no difference in the second decisions was observed due to weak anchoring. Anchoring also caused an order effect in trust and reciprocity, with higher trust when the take frame was played first, and higher reciprocity when the give frame was played first. Our results contribute to our knowledge about situational factors that shape trust and reciprocity, highlighting the impact of the context of the decision environment in terms of the impact of the order on framing.
]]>Games doi: 10.3390/g14020020
Authors: Tongxin Yin Armin Sarabi Mingyan Liu
In this paper, we present a game-theoretic analysis of ransomware. To this end, we provide theoretical and empirical analysis of a two-player Attacker-Defender (A-D) game, as well as a Defender-Insurer (D-I) game; in the latter, the attacker is assumed to be a non-strategic third party. Our model assumes that the defender can invest in two types of protection against ransomware attacks: (1) general protection through a deterrence effort, making attacks less likely to succeed, and (2) a backup effort serving the purpose of recourse, allowing the defender to recover from successful attacks. The attacker then decides on a ransom amount in the event of a successful attack, with the defender choosing to pay ransom immediately, or to try to recover their data first while bearing a recovery cost for this recovery attempt. Note that recovery is not guaranteed to be successful, which may eventually lead to the defender paying the demanded ransom. Our analysis of the A-D game shows that the equilibrium falls into one of three scenarios: (1) the defender will pay the ransom immediately without having invested any effort in backup, (2) the defender will pay the ransom while leveraging backups as a credible threat to force a lower ransom demand, and (3) the defender will try to recover data, only paying the ransom when recovery fails. We observe that the backup effort will be entirely abandoned when recovery is too expensive, leading to the (worst-case) first scenario which rules out recovery. Furthermore, our analysis of the D-I game suggests that the introduction of insurance leads to moral hazard as expected, with the defender reducing their efforts; less obvious is the interesting observation that this reduction is mostly in their backup effort.
]]>Games doi: 10.3390/g14020019
Authors: Garrison W. Greenwood Daniel Ashlock
Divide the dollar is a simplified version of a two player bargaining problem game devised by John Nash. The generalized divide the dollar game has n>2 players. Evolutionary algorithms can be used to evolve individual players for this generalized game but representation—i.e., a genome plus a move or search operator(s)—must be carefully chosen since it affects the search process. This paper proposes an entirely new representation called a demand matrix. Each individual in the evolving population now represents a collection of n players rather than just an individual player. Players use previous outcomes to decide their choices (bids) in the current round. The representation scales linearly with the number of players and the move operator is a variant of an evolution strategy. The results indicate that this proposed representation for the generalized divide the dollar game permits the efficient evolution of large player populations with high payoffs and fair demand sets.
]]>Games doi: 10.3390/g14010018
Authors: Elias Dinopoulos Constantinos Syropoulos Theofanis Tsoulouhas
The primary objective of this paper is to develop a two-country, dynamic, general equilibrium model with innovation contests to formally analyze the impact of globalization on the skill premium and fully-endogenous growth. Higher quality products are endogenously discovered through stochastic and sequential global innovation contests in which challengers devote resources to R&D, while technology leaders undertake rent-protection activities (RPAs) to prolong the expected duration of their temporary monopoly power by hindering the R&D effort of challengers. The model generates intra-sectoral trade, multinationals, and international outsourcing of investment services. Globalization, captured by a move from autarky to the integrated-world equilibrium, leads to convergence of wages and growth rates. Globalization and long-run growth are either substitutes or complements depending on a country’s relative skill abundance and the ranking of skill intensities between RPAs and R&D services. Trade openness between two countries that possess identical relative skill endowments but differ in size does not affect either country’s long-run growth.
]]>Games doi: 10.3390/g14010017
Authors: Sakura Arai Motoki Watabe Kei Kanari Qiulu Shou Frank Krueger Haruto Takagishi
Oxytocin has been proposed to regulate human trust. Previous experiments supported this claim by demonstrating that exogenous and endogenous oxytocin is associated with trust (how much trust people place in strangers) and reciprocity (how much people reciprocate when trusted). However, recent replication attempts have been unsuccessful in demonstrating the trust-enhancing effect of oxytocin, and there is limited evidence on whether oxytocin is associated with reciprocity. This study aimed to replicate the previously found nonlinear relationships between the endogenous oxytocin concentration and both trust and reciprocity by utilizing a monetarily incentivized trust game. In a college sample, we found that salivary oxytocin levels showed (i) an inverted U-shaped relationship with trust in men and (ii) a U-shaped relationship with reciprocity in women. The current results confirm the previous finding that endogenous oxytocin levels have nonlinear relationships with trust and reciprocity. Further research on the role of oxytocin secretion in trust and reciprocity is warranted.
]]>Games doi: 10.3390/g14010016
Authors: Yoshio Kamijo Teruyuki Tamura
The purpose of this study was to determine whether attitudes toward risk and altruism are affected by being in a group or being alone. In contrast to previous economic research on group decision-making, we excluded the effects of group informal discussions, which are thought to be a “black box” when individuals make decisions in a group. In this regard, the subjects in our experiment were only requested to show their faces to the other members, without further communication. Moreover, we adopted two collective decision rules, i.e., the median rule and the random rule, which provide the truth-telling mechanism. In the experiments of both anonymous investment and donation, we found that the subjects who made decisions in a group offered significantly lower amounts than those who made decisions alone, after controlling for individuals’ risk and altruistic preferences. The findings imply that people are more risk-averse and self-interested when they are in a group, regardless of which collective decision rules are adopted.
]]>Games doi: 10.3390/g14010015
Authors: Andrea Amelio Florian Zimmermann
Motivated reasoning refers to the idea that people hold certain beliefs about themselves or the world due to their desire to do so, rather than striving for accuracy. This type of belief formation can lead to overconfidence and polarization, as well as facilitate immoral behavior at both the individual and collective levels. One of the supply-side mechanisms for motivated reasoning is motivated memory, or the selective retrieval of past experiences or information based on self-serving criteria. In this article, we review the still young economics literature on motivated memory. Summarizing both theoretical and empirical work, we highlight the key results this literature has produced. We also discuss open questions and potentially exciting avenues for future research in this area.
]]>Games doi: 10.3390/g14010014
Authors: Guennady Ougolnitsky Anatoly Usov
We built and investigated analytically and numerically a differential game model of Cournot oligopoly with consideration of pollution for the general case and the case of symmetrical agents. We conducted a comparative analysis of selfish agents’ behavior (a differential game in normal form), their hierarchical organization (differential Stackelberg games), and cooperation (optimal control problem) using individual and collective indices of relative efficiency. The same analysis wasperformed for the models with the green effect when players chose both output volumes and environmental protection efforts. We used the Pontryagin maximum principle for analytical investigation and the method of qualitatively representative scenarios in simulation modeling for numerical calculations. This method allows for reducing the number of computer simulations, providing sufficient precision. As a result of the comparative analysis, systems of collective and individual preferences were obtained.
]]>Games doi: 10.3390/g14010013
Authors: Zhaobin Mo Xuan Di Rongye Shi
How to sample training/validation data is an important question for machine learning models, especially when the dataset is heterogeneous and skewed. In this paper, we propose a data sampling method that robustly selects training/validation data. We formulate the training/validation data sampling process as a two-player game: a trainer aims to sample training data so as to minimize the test error, while a validator adversarially samples validation data that can increase the test error. Robust sampling is achieved at the game equilibrium. To accelerate the searching process, we adopt reinforcement learning aided Monte Carlo trees search (MCTS). We apply our method to a car-following modeling problem, a complicated scenario with heterogeneous and random human driving behavior. Real-world data, the Next Generation SIMulation (NGSIM), is used to validate this method, and experiment results demonstrate the sampling robustness and thereby the model out-of-sample performance.
]]>Games doi: 10.3390/g14010012
Authors: Chenghan Zhou Andrew Spivey Haifeng Xu Thanh H. Nguyen
This paper studies the problem of information design in a general security game setting in which multiple self-interested defenders attempt to provide protection simultaneously for the same set of important targets against an unknown attacker. A principal, who can be one of the defenders, has access to certain private information (i.e., attacker type), whereas other defenders do not. We investigate the question of how that principal, with additional private information, can influence the decisions of the defenders by partially and strategically revealing her information. In particular, we develop a polynomial time ellipsoid algorithm to compute an optimal private signaling scheme. Our key finding is that the separation oracle in the ellipsoid approach can be carefully reduced to bipartite matching. Furthermore, we introduce a compact representation of any ex ante persuasive signaling schemes by exploiting intrinsic security resource allocation structures, enabling us to compute an optimal scheme significantly faster. Our experiment results show that by strategically revealing private information, the principal can significantly enhance the protection effectiveness for the targets.
]]>Games doi: 10.3390/g14010011
Authors: Games Editorial Office Games Editorial Office
High-quality academic publishing is built on a rigorous peer review process, and Games is no exception, upholding its high standards for published papers due to the outstanding efforts of our reviewers [...]
]]>Games doi: 10.3390/g14010010
Authors: Hester Sijtsma Nikki C. Lee Jacek Buczny Miriam Hollarek Reubs J. Walsh Mariët Van Buuren Lydia Krabbendam
Adolescence is an important developmental period for both trust behavior and personality maturation, and individual differences in trust decisions may be related to different personality traits. In the current study, a group of adolescents (n = 483, Mage = 13.5, SDage = 0.4) played two counterbalanced conditions of a multi-round trust game. In one condition, the partner displayed trustworthy behavior (the trustworthy condition), while the partner in the other condition played untrustworthy behavior (the untrustworthy condition). Three types of trust behavior were examined: initial trust behavior, the adaptation of trust behavior (trustworthy condition), and the adaptation of trust behavior (untrustworthy condition). Personality was measured using the Brief HEXACO Inventory. We expected the HEXACO personality dimensions of honesty–humility and agreeableness to be positively associated with initial trust behavior, but conscientiousness to be negatively related to initial trust behavior. The examination of the relationship between these dimensions and the adaptation of trust behavior were conducted on an exploratory basis. The investigation of the relationship between the remaining dimensions (emotionality, extraversion, and openness to experience) and the three types of trust behavior were also carried out on an exploratory basis. For each type of trust behavior, a hierarchical multiple regression analysis was undertaken to examine whether the HEXACO personality dimensions were related to trust behavior. Using frequentist analyses, no evidence was found that supported the HEXACO dimensions as significant predictors of the three types of trust behavior. Moreover, additional Bayesian analyses showed evidence that the hypothesized HEXACO dimensions (honesty–humility, agreeableness, and conscientiousness) did not outperform the non-hypothesized HEXACO dimensions (emotionality, extraversion, and openness to experience). The association between personality traits and trust might be less pronounced during adolescence as personality maturates across an individual’s lifespan. Additionally, due to a heightened sensitivity to the environment, contextual cues may affect adolescent decision-making processes, leaving less room for personality-driven behaviors.
]]>Games doi: 10.3390/g14010009
Authors: Foroogh Salekpay
Due to the challenge of global warming, the European Union (EU) signed the Paris Agreement (2015) to diminish total Greenhouse Gas (GHG) emissions. This paper addresses the conflict that EU member states face when they want to follow the target of the Paris Agreement for the period 2021–2030 which is a 55% GHG emission reduction by 2030 (compared with GHG emission in 1990). EU member states have to emit at a level that is lower than their emission needs. To solve this problem, we implement the claims problems approach as a method for distributing insufficient resources among parties with greater demands. We use several well-known division rules to divide the emission budget among EU member states. We define a set of principles that should be satisfied by division rules to select the most optimal allocation method. To diminish the effect of countries’ preferences on the allocation we use equity and stability criteria to examine the fairness of the rules. Moreover, we allocate the emission budget in two ways: First, we apply division rules to allocate the total emission budget for 2021–2030 among countries. Second, we allocate the emission budget annually from 2021 to 2030. We propose that Constrained Equal Awards (CEA) is an appropriate division rule to meet the target of 2030.
]]>Games doi: 10.3390/g14010008
Authors: Yao Zhang Yushu Zhang Yan Wu Frank Krueger
Trust and reciprocity promote cooperation and are key elements of a successful social life. This study investigated the framing effects on trust and reciprocity behaviors. Using an iterated one-shot within-subjects design, this study explored how trust and reciprocity decisions changed when the game was framed in terms of a give (i.e., using a standard trust game with a default of no trust) and a take (e.g., using a distrust game with a default of full trust) frame. Participants of both genders first completed the scenario version of the game (Session 1), and then played the roles of trustors (Session 2) and trustees (Session 3) with human and computer-mediated human partners either in the give or take frame. Our results showed increased trust in the give than in the take frame, but only pronounced in direct interaction with human (vs. indirect computer-mediated) partners. Participants also showed higher expectations of return in the give than in the take frame. The actual reciprocity was higher in the give than in the take frame when interacting both with human and computer-mediated human partners. The results contribute to our understanding of the factors that shape trust and reciprocity and emphasize the impact of framing the default.
]]>Games doi: 10.3390/g14010007
Authors: Todd Sandler
This paper considers the diverse public good characteristics of COVID-19 activities along with their strategic implications. The underlying aggregator technologies, which relate individual contributions to the amount consumed, affect the prognosis for the supply of COVID-related activities. Weakest-link activities assume a particularly pivotal role in curbing the spread of COVID-19. For instance, the propagation of COVID-19 through new strains is disproportionately influenced by those countries with the smallest vaccination rates or least isolation actions. Diverse income distribution among at-risk countries raises the need to “shore up” weakest-link countries’ provision to lift global supply. Generally, shoring-up actions result in a Prisoner’s Dilemma with unfavorable collective action prospects. As the number of countries requiring shoring up increases, the less favorable is the prospect for addressing provision shortfalls. Also, as the number of capable countries to do the shoring up increases, the prospect for successful action diminishes. The paper also examines the strategic implications of other aggregators—e.g., best shot and better shot—associated with COVID-inhibiting actions. To address best-shot anti-COVID actions, countries must pool or coordinate actions to meet a threshold. A host of institutions—e.g., the World Health Organization or public-private partnerships—can facilitate shoring-up weakest-link activities or coordinating best-shot actions.
]]>Games doi: 10.3390/g14010006
Authors: Arijit Mukherjee Yao Liu
Ignoring strategic interactions among final goods producers, the extant theoretical literature shows that lower costs of imported inputs increase the exports of the final goods using those inputs. Hence, it does not explain the empirically relevant positive relationship between the costs of imported inputs and the export of the final goods. We use a simple Cournot duopoly (i.e., duopoly quantity competition) with homogeneous products to show that if the exporters differ in input coefficients, lower costs of imported inputs may increase or decrease the exports of the final goods. Thus, we argue that strategic interdependence among the exporters can be an important factor for the positive relationship between lower costs of imported inputs and the export of the final goods. We further show that a lower cost of imported inputs may reduce the consumer surplus, total profits of the exporters, and world welfare. We also show the implications of a Bertrand duopoly (i.e., duopoly price competition) with horizontal product differentiation for our analysis.
]]>Games doi: 10.3390/g14010005
Authors: Heinrich H. Nax
First and foremost, pre-registration is not the all-in-one solution for experimental economics [...]
]]>Games doi: 10.3390/g14010004
Authors: Timothy Mathews Soiliou Daw Namoro James W. Boudreau
A multi-tournament environment is analyzed, focusing on the impact of organizer market structure on agent entry behavior. Two high ability agents first decide which tournament to enter (with fields then filled by low ability agents). If the marginal benefit of high ability agents in an event is weakly increasing, a monopsonist organizer sets prizes so that the high ability agents enter the same event. If this marginal benefit is diminishing, a monopsonist organizer will either: always set prizes for which the high ability agents enter different events; or set prizes for which the high ability agents enter different events if and only if the difference in ability between the high ability and low ability agents is sufficiently small. Sequentially competing organizers set prizes for which both high ability agents enter the same event if and only if the marginal benefit of having two high ability agents in one event is relatively large. For competing organizers there may be either a first or second mover advantage. Finally, Social Welfare may be higher or lower with competing organizers, implying greater organizer competition does not necessarily increase Social Welfare. Parallels are noted throughout to the labor market for professional golfers both over years when the PGA TOUR was essentially a monopsonist and more recently when LIV Golf emerged as a competitor.
]]>Games doi: 10.3390/g14010003
Authors: Iwan Bos Marco A. Marini
This paper examines a homogeneous-good Bertrand–Edgeworth oligopoly model to explore the role of firm size and number in pricing. We consider the price impact of merger, break up, investment, divestment, entry and exit. A merger leads to higher prices only when it increases the size of the largest seller and industry capacity is neither too big nor too small post-merger. Similarly, breaking up a firm only leads to lower prices when it concerns the biggest producer and aggregate capacity is within an intermediate range. Investment and entry (weakly) reduce prices, whereas divestment and exit yield (weakly) higher prices. Taken together, these findings suggest that size matters more than number in the determination of oligopoly prices.
]]>Games doi: 10.3390/g14010002
Authors: Arnaud Zlatko Dragicevic
This paper tries to prove that the outcomes stemming from interactions on assignment markets bring about coordination in case of a stochastic matching subject to various forms of expectations. We consider an exchange network with stochastic matching between the pairs of players and analyze the dynamics of bargaining in such a market. The cases of convergent expectations, divergent expectations and of social preferences are studied. The extension of earlier works lies in the consideration of a stochastic matching on a graph dependent on the weights of edges. The results show that, in all three cases, the dynamics converges rapidly to the generalized Nash bargaining solution, which is an equilibrium that combines notions of stability and fairness. In the first two scenarios, the numerical simulations reveal that the convergence toward a fixed point is speedily achieved at the value of the outside option. In the third scenario, the fixed point promptly converges to the value of the outside option supplemented by the surplus share.
]]>Games doi: 10.3390/g14010001
Authors: Roberto Andrade Iván Ortiz María Cazares Gustavo Navas María Isabel Sánchez-Pazmiño
The growth of the Internet of Things (IoT) has accelerated digital transformation processes in organizations and cities. However, it has also opened new security challenges due to the complexity and dynamism of these systems. The application of security risk analysis methodologies used to evaluate information technology (IT) systems have their limitations to qualitatively assess the security risks in IoT systems, due to the lack of historical data and the dynamic behavior of the solutions based on the IoT. The objective of this study is to propose a methodology for developing a security risk analysis using scenarios based on the risk factors of IoT devices. In order to manage the uncertainty due to the dynamics of IoT behaviors, we propose the use of Bayesian networks in conjunction with the Best Worst Method (BWM) for multi-criteria decision-making to obtain a quantitative security risk value.
]]>Games doi: 10.3390/g13060083
Authors: Alex Dickson Ian A. MacKenzie Petros G. Sekeris
We investigate observed rent dissipation—the ratio of the total costs of rent seeking to the monetary value of the rent—in winner-take-all and share contests, where preferences are more general than usually assumed in the literature. With concave valuation of the rent, we find that contests can exhibit observed over-dissipation if the contested rent is below a threshold and yet observed under-dissipation with large rents: the nature of preferences implies contestants are relatively effortful in contesting small rents. Considering more general preferences in contests thus allows us to reconcile the Tullock paradox—where rent-seeking levels are relatively small despite the contested rent being sizeable—with observed over-dissipation of rents in experimental settings, where contested rents are arguably small.
]]>Games doi: 10.3390/g13060082
Authors: Nora Grisáková Peter Štetka
The subject of this study is an oligopolistic market in which three firms operate in an environment of quantitative competition known as the Cournot oligopoly model. Firms and their production are differentiated, which brings the theoretical model closer to real market conditions. The main objective was to expand the Cournot duopoly and add another firm, resulting in an oligopolistic market structure assuming a partially differentiated production and coalition strategy between two firms. This article contains an oligopolistic model specifically designed for three different types of expectations, and has been applied to find and verify the stability of the net equilibrium of oligopolists. The market of telecommunication operators in Slovakia was selected as a real market case with accessible data on an oligopoly with three companies and partial differentiation. There are studies in which the authors limit their considerations to a certain number of repetitions of oligopolistic games. An infinite time interval is considered here. Three types of future expectations were considered: a simple dynamic model (or naïve expectations) in which the oligopolist assumes that its competitors will behave in the future based on their response functions, an adaptive expectations model in which the oligopolist considers a weighted average of the quantities offered by its competitors, and real expectations in which firms behave as rational players and do not have complete information about demand and offer output based on expected marginal profit. While the presented model proved to be stable under naïve and adaptive expectations, no stable equilibrium was found under real expectations and further results indicate a chaotic behavior.
]]>Games doi: 10.3390/g13060081
Authors: Thanh Hong Nguyen Amulya Yadav
In security games, the defender often has to predict the attacker’s behavior based on some observed attack data. However, a clever attacker can intentionally change its behavior to mislead the defender’s learning, leading to an ineffective defense strategy. This paper investigates the attacker’s imitative behavior deception under uncertainty, in which the attacker mimics a (deceptive) Quantal Response behavior model by consistently playing according to a certain parameter value of that model, given that it is uncertain about the defender’s actual learning outcome. We have three main contributions. First, we introduce a new maximin-based algorithm to compute a robust attacker deception decision under uncertainty, given the defender is unaware of the attacker deception. Our polynomial algorithm is built via characterizing the decomposability of the attacker deception space as well optimal deception behavior of the attacker against the worst case of uncertainty. Second, we propose a new counter-deception algorithm to tackle the attacker’s deception. We theoretically show that there is a universal optimal defense solution, regardless of any private knowledge the defender has about the relation between their learning outcome and the attacker deception choice. Third, we conduct extensive experiments in various security game settings, demonstrating the effectiveness of our proposed counter-deception algorithms to handle the attacker manipulation.
]]>Games doi: 10.3390/g13060080
Authors: Stefan Rass Sandra König Stefan Schauer
This article is an overview of recent progress on a theory of games, whose payoffs are probability distributions rather than real numbers, and which have their equilibria defined and computed over a (suitably restricted yet dense) set of distributions. While the classical method of defining game models with real-valued utility functions has proven strikingly successful in many domains, some use cases from the security area revealed shortcomings of the classical real-valued game models. These issues motivated the use of probability distributions as a more complex object to express revenues. The resulting class of games displays a variety of phenomena not encountered in classical games, such as games that have continuous payoff functions but still no equilibrium, or games that are zero-sum but for which fictitious play does not converge. We discuss suitable restrictions of how such games should be defined to allow the definition of equilibria, and show the notion of a lexicographic Nash equilibrium, as a proposed solution concept in this generalized class of games.
]]>Games doi: 10.3390/g13060079
Authors: Clelia Mazzoni Patrizia Sbriglia
In this paper, we present the results of an experiment conducted in Italy on trusting behaviour. Our subjects participated in a trust game and filled in a questionnaire on trust and trustworthiness based on the attitudinal questions reported in the European Value Survey. The aims of the research are twofold. Firstly, using the experimental dataset, we construct two measures of trustworthiness among all recipients in the experiment, one based on the questionnaires’ answers and another based on the strategy method. We then compare the ex-ante behavioural decision to trust (before participants are allocated to a group) with the ex-post decision to trust (after participants are allocated to a group and trustors are informed of the level of trustworthiness of all the recipients who have been randomly allocated to each group). Our main finding is that trust strongly varies once the information is disclosed to trustors. The effect on trust is greater when the strategy method is used. Secondly, we compare the behavioural measure of trust with the attitudinal measures of trust and trustworthiness and find that there is only a weak correlation between the two measures, thus confirming, for the Italian case, similar findings in country-based studies on trust.
]]>Games doi: 10.3390/g13060078
Authors: Achille Basile Anna De Simone Ciro Tarantino
Let Φn be the set of the binary strategy-proof social choice functions referred to a group of n voters who are allowed to declare indifference between the alternatives. We provide a recursive way to obtain the set Φn+1 from the set Φn. Computing the cardinalities |Φn| presents difficulties as the computation of the Dedekind numbers. The latter give the analogous number of social choice functions when only strict preferences are admitted. A comparison is given for the known values. Based on our results, we present a graphical description of the binary strategy-proof social choice functions in the case of three voters.
]]>Games doi: 10.3390/g13060077
Authors: Marina Bánnikova José-Manuel Giménez-Gómez
This paper studies how the cost of delay and voting order affect agents’ decisions in a unanimity voting mechanism. Specifically, we consider two-voter conclaves with commonly known preferences over two alternatives, the cost of delay, and the following novelty: each voter has a subjective deadline—a moment in time when he/she prefers immediate agreement on any alternative, rather than future agreement on his/her most-preferred alternative. Our key finding shows that patience is not necessarily a main attribute of strategic advantage. When the first voter is the same at every stage, this voter will obtain his/her preferred alternative, even if he/she is the least patient one. However, this first movement advantage disappears when agents alternate as the first voter of each stage: in this case, the most patient voter always wins.
]]>Games doi: 10.3390/g13060076
Authors: Maxwell N. Burton-Chellew Stuart A. West
The black box method was developed as an “asocial control” to allow for payoff-based learning while eliminating social responses in repeated public goods games. Players are told they must decide how many virtual coins they want to input into a virtual black box that will provide uncertain returns. However, in truth, they are playing with each other in a repeated social game. By “black boxing” the game’s social aspects and payoff structure, the method creates a population of self-interested but ignorant or confused individuals that must learn the game’s payoffs. This low-information environment, stripped of social concerns, provides an alternative, empirically derived null hypothesis for testing social behaviours, as opposed to the theoretical predictions of rational self-interested agents (Homo economicus). However, a potential problem is that participants can unwittingly affect the learning of other participants. Here, we test a solution to this problem in a range of public goods games by making participants interact, unknowingly, with simulated players (“computerised black box”). We find no significant differences in rates of learning between the original and the computerised black box, therefore either method can be used to investigate learning in games. These results, along with the fact that simulated agents can be programmed to behave in different ways, mean that the computerised black box has great potential for complementing studies of how individuals and groups learn under different environments in social dilemmas.
]]>Games doi: 10.3390/g13060075
Authors: Hiroki Shinozaki
We consider the problem of allocating heterogeneous objects to agents with money, where the number of agents exceeds that of objects. Each agent can receive at most one object, and some objects may remain unallocated. A bundle is a pair consisting of an object and a payment. An agent’s preference over bundles may not be quasi-linear, which exhibits income effects or reflects borrowing costs. We investigate the class of rules satisfying one of the central properties of fairness in the literature, egalitarian-equivalence, together with the other desirable properties. We propose (i) a novel class of rules that we call the independent second-prices rules with variable constraints and (ii) a novel condition on constraints that we call respecting the valuation coincidence. Then, we establish that the independent second-prices rule with variable constraints that respects the valuation coincidence is the only rule satisfying egalitarian-equivalence, strategy-proofness, individual rationality, and no subsidy for losers. Our characterization result implies that in the case of three or more agents, there are few opportunities for agents to receive objects under a rule satisfying egalitarian-equivalence and the other desirable properties, which highlights the strong tension between egalitarian-equivalence and efficiency. In contrast, in the case of two agents and a single object, egalitarian-equivalence is compatible with efficiency.
]]>Games doi: 10.3390/g13060074
Authors: Emin Karagözoğlu Elif Tosun
We experimentally investigated the effects of the possibility of taking in the dictator game and the choices of passive players between the dictator game and the taking game on the distribution decisions of active players. Our main findings support our hypothesis: when the dictator game is not exogenously given but chosen by the receivers (or passive players), this makes them accountable, which leads to less giving by dictators. We also conducted an online survey to gain further insights about our experimental results. Survey participants predicted most of the observed behavior in the experiment and explained the factors that might have driven the predicted behavior using reasoning similar to ours. Our results provide a new perspective for the dependence of giving in the dictator game on contextual factors.
]]>Games doi: 10.3390/g13060073
Authors: Zhuohan Wang Dong Hao
Revision game is a very recent advance in dynamic game theory and it can be used to analyze the trading in the pre-opening stock market. In such games, players prepare actions that will be implemented at a given deadline, before which they may have opportunities to revise actions. For the first time, we study the role of the deadline in revision games, which is the core component that distinguishes revision games from classic games. We introduce the deadline distribution into revision game model and characterize the sufficient and necessary condition for players’ strategies to constitute an equilibrium. The equilibrium strategy with respect to the deadline uncertainty is given by a simple differential equation set. Governed by this differential equation set, players initially fully cooperate, and the cooperation level decreases as time progresses. The uncertainty has a great impact on players’ behavior. As the uncertainty increases, players become more risk averse, in the sense that they prefer lower mutual cooperation rate rather than higher payoff with higher uncertainty. Specifically, they will not stay in full cooperation for a long time, while after they deviate from the full cooperation, they adjust their plans more slowly and cautiously. The deadline uncertainty can improve the competition and avoid collusion in games, which could be utilized for auction design and pre-opening stock market regulations.
]]>Games doi: 10.3390/g13060072
Authors: Giacomo Bonanno
We argue in favor of a departure from the equilibrium approach in game theory towards the less ambitious goal of describing only the actual behavior of rational players. The notions of Nash equilibrium and its refinements require a specification of the players’ choices and beliefs not only along the equilibrium play but also at counterfactual histories. We discuss an alternative—counterfactual-free—approach that focuses on choices and beliefs along the actual play, while being silent on choices and beliefs at unreached histories. Such an approach was introduced in an earlier paper that considered only perfect-information games. Here we extend the analysis to general extensive-form games (allowing for imperfect information) and put forward a behavioral notion of self-confirming play, which is close in spirit to the literature on self-confirming equilibrium. We also extend, to general extensive-form games, the characterization of rational play that is compatible with pure-strategy Nash equilibrium.
]]>Games doi: 10.3390/g13060071
Authors: Benjamin Young
We consider a market setting where a consumer holds either a naive or sophisticated perception of their preference over products. We introduce the concept of a cognitive equilibrium, in which the consumer can transition between the cognitive states of naiveté and sophistication depending on the degree of exploitation in the market. We compare market outcomes under monopoly and competition. While competition unambiguously improves market outcomes when the consumer’s cognitive state is exogenous, it can strictly lower gains from trade when cognitive states are endogenously determined.
]]>Games doi: 10.3390/g13060070
Authors: Reza Azad Gholami Leif Kristoffer Sandal Jan Ubøe
Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized supply channel members to devise optimal long-term (multi-period) supply, pricing, and timing strategies while catering to stochastic demand in a diverse set of market scenarios. Despite its ubiquity in potential applications, the time-dependent channel optimization problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing equilibrium problems. However, there are many scenarios where a single-period channel optimization solution may turn out to be myopic as it does not consider the after-effects of current pricing on future demand. To remedy this typical shortcoming, using general memory functions, we include the strategic customers’ cognitive bias toward pricing history in the supply channel equilibrium problem. In the form of two constructive theorems, we provide explicit solution algorithms for the ensuing Nash–Stackelberg equilibrium problems. In particular, we prove that our recursive solution algorithm can find equilibria in the multi-periodic variation of many standard supply channel contracts such as wholesale, buyback, and revenue-sharing contracts.
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