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Information Theory in Game Theory
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Information Theory in Game Theory

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (28 February 2018) | Viewed by 51826

Special Issue Editors

Prof. Dr. Pasquale Malacaria

E-Mail Website
Guest Editor
School of Electronic Engineering and Computer Science, Queen Mary University of London, London E1 4NS, UK
Interests: Information Theory; Security; Software analysis and Verification; Game Theory; Decision Support
Dr. MHR Khouzani

E-Mail Website
Guest Editor
School of Electronic Engineering and Computer Science, Queen Mary University of London, London E1 4NS, UK
Interests: Game Theory; Information Theory; Convex Optimization; Security, Networks; Decision Support

Special Issue Information

Dear Colleagues,

Information theory, as the mathematics of communication and storage of information, and game theory, seen as the mathematics of adversarial and cooperative interaction, have a potentially large synergy.

Many problems can be studied at the intersection of these two disciplines. Examples are network problems, where sharing bandwidth between agents can be seen as a game of information. Another case of interest is security, for example, where one wants to minimize the leakage of information in an adversarial setting. In other applications like machine learning, one may want, instead, to maximize the information that can be extracted in a cooperative or adversarial setting. The intersection goes beyond classical information theory: For example, game theory may be relevant when studying quantum information problems.

For this Special Issue we solicit contributions advancing the state-of-the-art at the intersection of game and information theory. We are particularly interested in foundational work (classical and quantum information) and more applied work with a principled methodology rooted in these disciplines.

Prof. Dr. Pasquale  Malacaria
Dr. MHR  Khouzani
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Classical and quantum information theory

  • Adversarial and cooperative game theory

  • Machine learning

  • Security

  • Networks

  • Economics

  • Applications of information and game theory

Published Papers (12 papers)

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Editorial

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2 pages, 129 KiB  
Editorial
Information Theory in Game Theory
by MHR Khouzani and Pasquale Malacaria
Entropy 2018, 20(11), 817; https://doi.org/10.3390/e20110817 - 24 Oct 2018
Cited by 1 | Viewed by 3296
Abstract
Information theory, as the mathematics of communication and storage of information, and game theory, as the mathematics of adversarial and cooperative strategic behaviour, are each successful fields of research on their own. [...] Full article
(This article belongs to the Special Issue Information Theory in Game Theory)

Research

Jump to: Editorial

19 pages, 1613 KiB  
Article
From Nash Equilibria to Chain Recurrent Sets: An Algorithmic Solution Concept for Game Theory
by Christos Papadimitriou and Georgios Piliouras
Entropy 2018, 20(10), 782; https://doi.org/10.3390/e20100782 - 12 Oct 2018
Cited by 12 | Viewed by 5368
Abstract
In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point [...] Read more.
In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point theorem, the most sophisticated result in his era’s topology—in fact, recent algorithmic work has established that Nash equilibria are computationally equivalent to fixed points. In this paper, we propose a new class of universal non-equilibrium solution concepts arising from an important theorem in the topology of dynamical systems that was unavailable to Nash. This approach starts with both a game and a learning dynamics, defined over mixed strategies. The Nash equilibria are fixpoints of the dynamics, but the system behavior is captured by an object far more general than the Nash equilibrium that is known in dynamical systems theory as chain recurrent set. Informally, once we focus on this solution concept—this notion of “the outcome of the game”—every game behaves like a potential game with the dynamics converging to these states. In other words, unlike Nash equilibria, this solution concept is algorithmic in the sense that it has a constructive proof of existence. We characterize this solution for simple benchmark games under replicator dynamics, arguably the best known evolutionary dynamics in game theory. For (weighted) potential games, the new concept coincides with the fixpoints/equilibria of the dynamics. However, in (variants of) zero-sum games with fully mixed (i.e., interior) Nash equilibria, it covers the whole state space, as the dynamics satisfy specific information theoretic constants of motion. We discuss numerous novel computational, as well as structural, combinatorial questions raised by this chain recurrence conception of games. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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20 pages, 367 KiB  
Article
Optimal Channel Design: A Game Theoretical Analysis
by MHR. Khouzani and Pasquale Malacaria
Entropy 2018, 20(9), 675; https://doi.org/10.3390/e20090675 - 05 Sep 2018
Cited by 6 | Viewed by 3183
Abstract
This paper studies the problem of optimal channel design. For a given input probability distribution and for hard and soft design constraints, the aim here is to design a (probabilistic) channel whose output leaks minimally from its input. To analyse this problem, general [...] Read more.
This paper studies the problem of optimal channel design. For a given input probability distribution and for hard and soft design constraints, the aim here is to design a (probabilistic) channel whose output leaks minimally from its input. To analyse this problem, general notions of entropy and information leakage are introduced. It can be shown that, for all notions of leakage here defined, the optimal channel design problem can be solved using convex programming with zero duality gap. Subsequently, the optimal channel design problem is studied in a game-theoretical framework: games allow for analysis of optimal strategies of both the defender and the adversary. It is shown that all channel design problems can be studied in this game-theoretical framework, and that the defender’s Bayes–Nash equilibrium strategies are equivalent to the solutions of the convex programming problem. Moreover, the adversary’s equilibrium strategies correspond to a robust inference problem. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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43 pages, 639 KiB  
Article
A Game-Theoretic Approach to Information-Flow Control via Protocol Composition
by Mário S. Alvim, Konstantinos Chatzikokolakis, Yusuke Kawamoto and Catuscia Palamidessi
Entropy 2018, 20(5), 382; https://doi.org/10.3390/e20050382 - 18 May 2018
Cited by 9 | Viewed by 3852
Abstract
In the inference attacks studied in Quantitative Information Flow (QIF), the attacker typically tries to interfere with the system in the attempt to increase its leakage of secret information. The defender, on the other hand, typically tries to decrease leakage by introducing some [...] Read more.
In the inference attacks studied in Quantitative Information Flow (QIF), the attacker typically tries to interfere with the system in the attempt to increase its leakage of secret information. The defender, on the other hand, typically tries to decrease leakage by introducing some controlled noise. This noise introduction can be modeled as a type of protocol composition, i.e., a probabilistic choice among different protocols, and its effect on the amount of leakage depends heavily on whether or not this choice is visible to the attacker. In this work, we consider operators for modeling visible and hidden choice in protocol composition, and we study their algebraic properties. We then formalize the interplay between defender and attacker in a game-theoretic framework adapted to the specific issues of QIF, where the payoff is information leakage. We consider various kinds of leakage games, depending on whether players act simultaneously or sequentially, and on whether or not the choices of the defender are visible to the attacker. In the case of sequential games, the choice of the second player is generally a function of the choice of the first player, and his/her probabilistic choice can be either over the possible functions (mixed strategy) or it can be on the result of the function (behavioral strategy). We show that when the attacker moves first in a sequential game with a hidden choice, then behavioral strategies are more advantageous for the defender than mixed strategies. This contrasts with the standard game theory, where the two types of strategies are equivalent. Finally, we establish a hierarchy of these games in terms of their information leakage and provide methods for finding optimal strategies (at the points of equilibrium) for both attacker and defender in the various cases. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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12 pages, 791 KiB  
Article
Password Security as a Game of Entropies
by Stefan Rass and Sandra König
Entropy 2018, 20(5), 312; https://doi.org/10.3390/e20050312 - 25 Apr 2018
Cited by 15 | Viewed by 5851
Abstract
We consider a formal model of password security, in which two actors engage in a competition of optimal password choice against potential attacks. The proposed model is a multi-objective two-person game. Player 1 seeks an optimal password choice policy, optimizing matters of memorability [...] Read more.
We consider a formal model of password security, in which two actors engage in a competition of optimal password choice against potential attacks. The proposed model is a multi-objective two-person game. Player 1 seeks an optimal password choice policy, optimizing matters of memorability of the password (measured by Shannon entropy), opposed to the difficulty for player 2 of guessing it (measured by min-entropy), and the cognitive efforts of player 1 tied to changing the password (measured by relative entropy, i.e., Kullback–Leibler divergence). The model and contribution are thus twofold: (i) it applies multi-objective game theory to the password security problem; and (ii) it introduces different concepts of entropy to measure the quality of a password choice process under different angles (and not a given password itself, since this cannot be quality-assessed in terms of entropy). We illustrate our approach with an example from everyday life, namely we analyze the password choices of employees. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
17 pages, 1230 KiB  
Article
Location-Aware Incentive Mechanism for Traffic Offloading in Heterogeneous Networks: A Stackelberg Game Approach
by Kailing Yao, Yunpeng Luo, Yang Yang, Xin Liu, Yuli Zhang and Changhua Yao
Entropy 2018, 20(4), 302; https://doi.org/10.3390/e20040302 - 20 Apr 2018
Cited by 5 | Viewed by 3343
Abstract
This article investigates the traffic offloading problem in the heterogeneous network. The location of small cells is considered as an important factor in two aspects: the amount of resources they share for offloaded macrocell users and the performance enhancement they bring after offloading. [...] Read more.
This article investigates the traffic offloading problem in the heterogeneous network. The location of small cells is considered as an important factor in two aspects: the amount of resources they share for offloaded macrocell users and the performance enhancement they bring after offloading. A location-aware incentive mechanism is therefore designed to incentivize small cells to serve macrocell users. Instead of taking the amount of resources shared as the basis of the reward division, the performance promotion brought to the macro network is taken. Meanwhile, in order to ensure the superiority of small cell users, the significance of them weighs heavier than macrocell users instead of being treated equally. The offloading problem is formulated as a Stackelberg game where the macro cell base station is the leader and small cells are followers. The Stackelberg equilibrium of the game is proved to be existing and unique. It is also proved to be the optimum of the proposed problem. Simulation and numerical results verify the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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17 pages, 6099 KiB  
Article
A Co-Opetitive Automated Negotiation Model for Vertical Allied Enterprises Teams and Stakeholders
by Taiguang Gao, Qing Wang, Min Huang, Xingwei Wang and Yu Zhang
Entropy 2018, 20(4), 286; https://doi.org/10.3390/e20040286 - 14 Apr 2018
Cited by 3 | Viewed by 4928
Abstract
Upstream and downstream of supply chain enterprises often form a tactic vertical alliance to enhance their operational efficiency and maintain their competitive edges in the market. Hence, it is critical for an alliance to collaborate over their internal resources and resolve the profit [...] Read more.
Upstream and downstream of supply chain enterprises often form a tactic vertical alliance to enhance their operational efficiency and maintain their competitive edges in the market. Hence, it is critical for an alliance to collaborate over their internal resources and resolve the profit conflicts among members, so that the functionality required by stakeholders can be fulfilled. As an effective solution, automated negotiation for the vertical allied enterprises team and stakeholder will sufficiently make use of emerging team advantages and significantly reduce the profit conflicts in teams with grouping decisions rather than unilateral decisions by some leader. In this paper, an automated negotiation model is designed to describe both the collaborative game process among the team members and the competitive negotiation process between the allied team and the stakeholder. Considering the co-competitiveness of the vertical allied team, the designed model helps the team members making decision for their own sake, and the team counter-offers for the ongoing negotiation are generated with non-cooperative game process, where the profit derived from negotiation result is distributed with Shapley value method according to contribution or importance contributed by each team member. Finally, a case study is given to testify the effectiveness of the designed model. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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20 pages, 1010 KiB  
Article
Nash Bargaining Game-Theoretic Framework for Power Control in Distributed Multiple-Radar Architecture Underlying Wireless Communication System
by Chenguang Shi, Fei Wang, Sana Salous, Jianjiang Zhou and Zhentao Hu
Entropy 2018, 20(4), 267; https://doi.org/10.3390/e20040267 - 11 Apr 2018
Cited by 20 | Viewed by 4420
Abstract
This paper presents a novel Nash bargaining solution (NBS)-based cooperative game-theoretic framework for power control in a distributed multiple-radar architecture underlying a wireless communication system. Our primary objective is to minimize the total power consumption of the distributed multiple-radar system (DMRS) with the [...] Read more.
This paper presents a novel Nash bargaining solution (NBS)-based cooperative game-theoretic framework for power control in a distributed multiple-radar architecture underlying a wireless communication system. Our primary objective is to minimize the total power consumption of the distributed multiple-radar system (DMRS) with the protection of wireless communication user’s transmission, while guaranteeing each radar’s target detection requirement. A unified cooperative game-theoretic framework is proposed for the optimization problem, where interference power constraints (IPCs) are imposed to protect the communication user’s transmission, and a minimum signal-to-interference-plus-noise ratio (SINR) requirement is employed to provide reliable target detection for each radar. The existence, uniqueness and fairness of the NBS to this cooperative game are proven. An iterative Nash bargaining power control algorithm with low computational complexity and fast convergence is developed and is shown to converge to a Pareto-optimal equilibrium for the cooperative game model. Numerical simulations and analyses are further presented to highlight the advantages and testify to the efficiency of our proposed cooperative game algorithm. It is demonstrated that the distributed algorithm is effective for power control and could protect the communication system with limited implementation overhead. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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15 pages, 472 KiB  
Article
Game Theoretic Approach for Systematic Feature Selection; Application in False Alarm Detection in Intensive Care Units
by Fatemeh Afghah, Abolfazl Razi, Reza Soroushmehr, Hamid Ghanbari and Kayvan Najarian
Entropy 2018, 20(3), 190; https://doi.org/10.3390/e20030190 - 12 Mar 2018
Cited by 12 | Viewed by 4508
Abstract
Intensive Care Units (ICUs) are equipped with many sophisticated sensors and monitoring devices to provide the highest quality of care for critically ill patients. However, these devices might generate false alarms that reduce standard of care and result in desensitization of caregivers to [...] Read more.
Intensive Care Units (ICUs) are equipped with many sophisticated sensors and monitoring devices to provide the highest quality of care for critically ill patients. However, these devices might generate false alarms that reduce standard of care and result in desensitization of caregivers to alarms. Therefore, reducing the number of false alarms is of great importance. Many approaches such as signal processing and machine learning, and designing more accurate sensors have been developed for this purpose. However, the significant intrinsic correlation among the extracted features from different sensors has been mostly overlooked. A majority of current data mining techniques fail to capture such correlation among the collected signals from different sensors that limits their alarm recognition capabilities. Here, we propose a novel information-theoretic predictive modeling technique based on the idea of coalition game theory to enhance the accuracy of false alarm detection in ICUs by accounting for the synergistic power of signal attributes in the feature selection stage. This approach brings together techniques from information theory and game theory to account for inter-features mutual information in determining the most correlated predictors with respect to false alarm by calculating Banzhaf power of each feature. The numerical results show that the proposed method can enhance classification accuracy and improve the area under the ROC (receiver operating characteristic) curve compared to other feature selection techniques, when integrated in classifiers such as Bayes-Net that consider inter-features dependencies. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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12 pages, 309 KiB  
Article
Entropy Affects the Competition of Ordered Phases
by Balázs Király and György Szabó
Entropy 2018, 20(2), 115; https://doi.org/10.3390/e20020115 - 10 Feb 2018
Cited by 3 | Viewed by 3199
Abstract
The effect of entropy at low noises is investigated in five-strategy logit-rule-driven spatial evolutionary potential games exhibiting two-fold or three-fold degenerate ground states. The non-zero elements of the payoff matrix define two subsystems which are equivalent to an Ising or a three-state Potts [...] Read more.
The effect of entropy at low noises is investigated in five-strategy logit-rule-driven spatial evolutionary potential games exhibiting two-fold or three-fold degenerate ground states. The non-zero elements of the payoff matrix define two subsystems which are equivalent to an Ising or a three-state Potts model depending on whether the players are constrained to use only the first two or the last three strategies. Due to the equivalence of these models to spin systems, we can use the concepts and methods of statistical physics when studying the phase transitions. We argue that the greater entropy content of the Ising phase plays an important role in its stabilization when the magnitude of the Potts component is equal to or slightly greater than the strength of the Ising component. If the noise is increased in these systems, then the presence of the higher entropy state can cause a kind of social dilemma in which the players’ average income is reduced in the stable Ising phase following a first-order phase transition. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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22 pages, 893 KiB  
Article
Traffic Offloading in Unlicensed Spectrum for 5G Cellular Network: A Two-Layer Game Approach
by Yan Li and Shaoyi Xu
Entropy 2018, 20(2), 88; https://doi.org/10.3390/e20020088 - 28 Jan 2018
Cited by 6 | Viewed by 4168
Abstract
Licensed Assisted Access (LAA) is considered one of the latest groundbreaking innovations to provide high performance in future 5G. Coexistence schemes such as Listen Before Talk (LBT) and Carrier Sensing and Adaptive Transmission (CSAT) have been proven to be good methods to share [...] Read more.
Licensed Assisted Access (LAA) is considered one of the latest groundbreaking innovations to provide high performance in future 5G. Coexistence schemes such as Listen Before Talk (LBT) and Carrier Sensing and Adaptive Transmission (CSAT) have been proven to be good methods to share spectrums, and they are WiFi friendly. In this paper, a modified LBT-based CSAT scheme is proposed which can effectively reduce the collision at the moment when Long Term Evolution (LTE) starts to transmit data in CSAT mode. To make full use of the valuable spectrum resources, the throughput of both LAA and WiFi systems should be improved. Thus, a two-layer Coalition-Auction Game-based Transaction (CAGT) mechanism is proposed in this paper to optimize the performance of the two systems. In the first layer, a coalition among Access Points (APs) is built to balance the WiFi stations and maximize the WiFi throughput. The main idea of the devised coalition forming is to merge the light-loaded APs with heavy-loaded APs into a coalition; consequently, the data of the overloaded APs can be offloaded to the light-loaded APs. Next, an auction game between the LAA and WiFi systems is used to gain a win–win strategy, in which, LAA Base Station (BS) is the auctioneer and AP coalitions are bidders. Thus, the throughput of both systems are improved. Simulation results demonstrate that the proposed scheme in this paper can improve the performance of both two systems effectively. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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12 pages, 10006 KiB  
Article
Strategic Information Processing from Behavioural Data in Iterated Games
by Michael S. Harré
Entropy 2018, 20(1), 27; https://doi.org/10.3390/e20010027 - 04 Jan 2018
Cited by 6 | Viewed by 3688
Abstract
Iterated games are an important framework of economic theory and application, at least since the original work of Axelrod’s computational tournaments of the early 80’s. Recent theoretical results have shown that games (the economic context) and game theory (the decision-making process) are both [...] Read more.
Iterated games are an important framework of economic theory and application, at least since the original work of Axelrod’s computational tournaments of the early 80’s. Recent theoretical results have shown that games (the economic context) and game theory (the decision-making process) are both formally equivalent to computational logic gates. Here these results are extended to behavioural data obtained from an experiment in which rhesus monkeys sequentially played thousands of the “matching pennies” game, an empirical example similar to Axelrod’s tournaments in which algorithms played against one another. The results show that the monkeys exhibit a rich variety of behaviours, both between and within subjects when playing opponents of varying complexity. Despite earlier suggestions, there is no clear evidence that the win-stay, lose-switch strategy is used, however there is evidence of non-linear strategy-based interactions between the predictors of future choices. It is also shown that there is consistent evidence across protocols and across individuals that the monkeys extract non-markovian information, i.e., information from more than just the most recent state of the game. This work shows that the use of information theory in game theory can test important hypotheses that would otherwise be more difficult to extract using traditional statistical methods. Full article
(This article belongs to the Special Issue Information Theory in Game Theory)
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