Games, Volume 13, Issue 5 (October 2022) – 12 articles

We investigate the strategic nature of farmers’ groundwater usage with a rich dataset from the American Midwest. We propose a new revealed preference test for the groundwater interaction as a dynamic game. We reject a view of groundwater usage decisions as strategic substitutes in favor of strategic complements as a better description. Full article

We test whether the decisions in a common-pool resource game are better modeled game-theoretically as strategic substitutes or complements using an individual-level dataset of groundwater usage that accounts for 3% of US irrigated agriculture. Based on a regression framework with instrumental variables, we find support for strategic complements, suggesting that reciprocity– and/or race-to-depletion–like dynamics are key to understanding groundwater usage. Full article

We consider a clearing problem in peer-to-peer energy markets, where prosumers can trade energy among each other and with the main grid to meet their energy demands. By using a game-theoretic formulation and exploiting operator-theoretic methods for generalized Nash equilibrium seeking, we propose two variants of the state-of-the-art distributed market clearing mechanism with improved convergence speeds. Furthermore, we design a third variant that allows for equilibrium selection, i.e., computing a specific market solution based on a convex preference function of the network operator, e.g., a congestion cost. We provide convergence guarantees and numerically show the advantages of our proposed algorithms in terms of convergence speed up and obtaining reduced grid congestion. Full article

We investigate whether tournament prizes that depend on joint output (“variable prize tournaments”) can alleviate the sabotage problem which is otherwise inherent in tournament structures. In a game-theoretical model with three contestants, we compare fixed-prize tournaments with tournaments where prizes depend on contestants’ joint output. Our analysis suggests that the incentives to sabotage in a fixed-prize tournament may be counteracted in a variable-prize tournament such that contestants no longer sabotage, but help one another. We empirically test the implications of our model with the help of a classroom experiment where we compare participants’ choices in a fixed-prize treatment ($FP$) with those of a variable-prize treatment ($VP$) in a between-subjects design. Given our parametrization, we expect efforts to be identical in both treatments, and we expect sabotage in the $FP$ treatment and no sabotage in the $VP$ treatment. In accordance with the model, we find that participants in the fixed-prize tournament sabotage one another, whereas participants in the variable-prize tournament help one another. At the same time, participants’ effort levels do not vary between the two treatments. Full article

We study two-sided matching contests with two sets, A and B, each of which includes a finite number of heterogeneous agents with commonly known types. The agents in each set compete in a lottery (Tullock) contest, and then are assortatively matched, namely, the winner of set A is matched with the winner of set B and so on until all the agents in the set with the smaller number of agents are matched. Each agent has a match value that depends on their own type and the type of their match. We assume that the agents’ efforts do not affect their match values and that they have a positive effect on welfare. Therefore, an interior equilibrium in which at least some of the agents are active is welfare superior to a corner equilibrium in which the agents choose to be non-active. We analyze the conditions under which there exists a (partial) interior equilibrium where at least some of the agents compete against each other and exert positive efforts. Full article

Why do some incomplete information markets feature intermediaries while others do not? I study the allocation of two goods in an incomplete information setting with a single principal, multiple agents with unit demand, and interdependent valuations. I construct a novel dynamic mechanism implemented by a principal who faces a set of intermediaries, each of whom represents an ex ante identical set of agents. This mechanism has a unique (up to permutation) weak perfect Bayesian equilibrium. The dynamic mechanism is inefficient with positive probability. Nevertheless, under mild conditions the agents are ex ante better off under the dynamic mechanism relative to a Vickrey-like auction because the intermediaries are more able to exploit information asymmetries in the dynamic mechanism than agents are able to exploit information asymmetries in the Vickrey-like auction. Finally, I show that in large markets the dynamic mechanism and Vickrey-like auction have the same expected total surplus. The comparison between the two mechanisms gives a stylized intuition for the hierarchical structure of larger markets and institutions. Full article

We study asymmetric second-price auctions under incomplete information. The bidders have two potentially different, commonly known, valuations for the object and private information about their entry costs. The seller, however, does not benefit from these entry costs. We calculate the equilibrium strategies of the bidders and analyze the optimal design for the seller in this environment in terms of expected entry and the number of potential bidders. Full article

We introduce a new mechanism for call auctions which are widely used in stock exchanges. Our unique design incorporates contingent claims (buy stock A, if selling stock B) into the price discovery process. With our proposed mechanism, we show that higher liquidity during the call auctions is achieved, as well as lower volatility after the call auctions. Moreover, we show that current call auctions and the proposed mechanism have similar incentive properties. Hence, we argue that the proposed mechanism would be an improvement over the existing opening auction rules at stock exchanges. Full article

Social learning often occurs between groups with different levels of experience. Yet little is known about the ideal behavioral rules in such contexts. Existing insights only apply when individuals learn from each other in the same group. In this paper, we close this gap and consider two groups, novices and experienced. Experienced should not learn from novices. For novices learning from experienced, a particular form of probabilistic imitation is selected. Novices should imitate any experienced who is more successful, and sometimes but not always imitate an experienced who is less successful. Full article

Trust is crucial to establishing reciprocal, positive social interactions and seems to be compromised in psychosis. The trust game offers methods to assess an individual’s trust responses to trust-reciprocating, positive feedback. Various computational techniques have been implemented to measure trust responsiveness, mostly based on investments. Here, we propose a new method, focusing on feedback response. Psychosis patients show social dysfunction and reduced trust during early and more progressed illness stages. The present study inspects differences in feedback responsiveness of 102 first-episode psychosis patients (FEPs), 43 chronic psychosis patients (CPs), and 39 healthy controls (HCs) by adopting a novel assessment approach. Additionally, baseline trust, the trust exerted without any prior knowledge of the partner’s trustworthiness, and mean trust were examined. Participants performed a multi-round trust game, playing the investor role, and were paired with a computer, programmed to return at least the invested amount, representing a trustworthy partner. The new method detected group differences, more distinguished than the former methods. Contrary to our expectations, baseline trust was intact in patients. Relative to HCs, patients were less responsive to feedback, failing to integrate the positive information into their decision-making process. The magnitude of returns was not associated with increases in trust. This novel method showed promising results and confirmed patients’ deficits within the social interactional domain. Full article

A qualitative game describes a situation in which antagonistic players strive to keep the evolutions of their state variables in predetermined constraint sets. We argue that a qualitative game model is a suitable mathematical representation of the struggle between a domestic central bank of a small open economy and a foreign central bank of a large economy to maintain their respective state variables within an acceptable band regardless of the other player’s choices. The actions of the foreign central bank affect the domestic exchange rate and, hence, domestic inflation, output gap and interest rate. However, these actions do not necessarily aim to destabilise the small open economy, nor do they take into account the state of the latter. The domestic bank’s problem, therefore, is similar to that of a game against nature. We refer to this type of qualitative game as a nuisance-agent game (or NA-game). We use viability theory to derive satisficing rules (in the sense of Simon) of nominal interest-rate adjustments for the domestic central bank of a small open economy in a qualitative NA-game against the foreign central bank. Full article

This paper analyzes the choice between quality improvements and copyright litigation by a proprietary seller who faces a competitive threat from a content-sharing platform. The platform operates like a “public good” with contributors who share content and free-riders who only consume content while adding to congestion on the platform. When the proprietor can identify contributors in the platform with sufficient accuracy, a litigation strategy that targets contributors exacerbates free-riding behavior in the sharing platform and drives down platform quality. In contrast, investing in quality improvements for the copyrighted good does not affect contribution decisions on the platform, leading to a uniform decrease in the relative payoff for all users on the platform. The model presented in the paper shows that the proprietor finds litigation more profitable than quality improvements if she can target contributors accurately. Welfare analysis of the model shows that the proprietor has too high an incentive to invest in litigation and inefficiently low incentives for quality improvements of the copyrighted good. Full article