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Michihiro Kandori - One of the best experts on this subject based on the ideXlab platform.
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Weakly Belief‐Free Equilibria in Repeated Games With Private Monitoring
Econometrica, 2011Co-Authors: Michihiro KandoriAbstract:Repeated Games with imperfect private monitoring have a wide range of applications, but a complete characterization of all equilibria in this class of Games has yet to be obtained. The existing literature has identified a relatively tractable subset of equilibria. The present paper introduces the notion of weakly belief-free equilibria for Repeated Games with imperfect private monitoring. This is a tractable class which subsumes, as a special case, a major part of the existing literature (the belief-free equilibria). It is shown that this class can outperform the equilibria identified by the previous work.
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Weakly Belief-Free Equilibria in Repeated Games with Private Monitoring
CIRJE F-Series, 2007Co-Authors: Michihiro KandoriAbstract:Repeated Games with imperfect private monitoring have a wide range of applications, but a complete characterization of all equilibria in this class of Games has yet to be obtained. The existing literature has identified a relatively tractable subset of equilibria. The present paper introduces the notion of weakly belief-free equilibria for Repeated Games with imperfect private monitoring. This is a tractable class which subsumes, as a special case, a major part of the existing literature (the belief-free equilibria), and it is shown that this class can outperform the equilibria identified by the previous work.
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Efficiency in Repeated Games Revisited: The Role of Private Strategies
Econometrica, 2006Co-Authors: Michihiro Kandori, Ichiro ObaraAbstract:Most theoretical or applied research on Repeated Games with imperfect monitoring has focused on public strategies: strategies that depend solely on the history of publicly observable signals. This paper sheds light on the role of private strategies: strategies that depend not only on public signals, but also on players' own actions in the past. Our main finding is that players can sometimes make better use of information by using private strategies and that efficiency in Repeated Games can be improved. Our equilibrium private strategy for Repeated prisoners' dilemma Games consists of two states and has the property that each player's optimal strategy is independent of the other player's state.
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Efficiency in Repeated Games Revisited: The Role of Private Strategies*
2003Co-Authors: Michihiro Kandori, Ichiro ObaraAbstract:Most theoretical or applied research on Repeated Games with imperfect monitoring has restricted attention to public strategies; strategies that only depend on history of publicly observable signals, and perfect public equilibrium (PPE); sequential equilibrium in public strategies. The present paper sheds light on the role of private strategies; strategies that depend on players' own actions in the past as well as observed public signals. Our main finding is that players can sometimes make better use of information by using private strategies and efficiency in Repeated Games can often be drastically improved. We illustrate this for both Games with a small signal space (Anti-folk theorem example) and Games with a large signal space, for which the Folk Theorem holds. Our private strategy can be regarded as a machine which consists of two states. We provide two di erent characterizations of our two-state machine equilibrium for general two-person Repeated Games with imperfect public monitoring.
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Introduction to Repeated Games with Private Monitoring
Journal of Economic Theory, 2002Co-Authors: Michihiro KandoriAbstract:Abstract We present a brief overview of recent developments in discounted Repeated Games with (imperfect) private monitoring. The literature explores the possibility of cooperation in a long-term relationship, where each agent receives imperfect private information about the opponents' actions. Although this class of Games admits a wide range of applications such as collusion under secret price-cutting, exchange of goods with uncertain quality, and observation errors, it has fairly complex mathematical structure due to the lack of common information shared by players. This is in sharp contrast to the well-explored case of Repeated Games under public information (with the celebrated Folk Theorems), and until recently little had been known about the private monitoring case. However, rapid developments in the past few years have revealed the possibility of cooperation under private monitoring for some class of Games. Journal of Economic Literature Classification Numbers: C72, C73, D43, D82, L13, L41.
John H. Nachbar - One of the best experts on this subject based on the ideXlab platform.
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Beliefs in Repeated Games
Econometrica, 2005Co-Authors: John H. NachbarAbstract:Consider a two-player discounted infinitely Repeated game. A player's belief is a probability distribution over the opponent's Repeated game strategies. This paper shows that, for a large class of Repeated Games, there are no beliefs that satisfy three properties: learnability, a diversity of belief condition called CSP, and consistency. Loosely, if players learn to forecast the path of play whenever each plays a strategy that the other anticipates (in the sense of being in the support of that player's belief) and if the sets of anticipated strategies are sufficiently rich, then neither anticipates any of his opponent's best responses. This generalizes results in Nachbar (1997).
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Beliefs in Repeated Games
SSRN Electronic Journal, 2003Co-Authors: John H. NachbarAbstract:Consider a two-player discounted infinitely Repeated game. A player's belief is a probability distribution over the opponent's Repeated game strategies. This paper shows that, for a large class of Repeated Games, there are no beliefs that satisfy three conditions, learnability, consistency, and a diversity condition, CS. This impossibility theorem generalizes results in Nachbar (1997).
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Bayesian learning in Repeated Games of incomplete information
Social Choice and Welfare, 2001Co-Authors: John H. NachbarAbstract:In Nachbar [20] and, more definitively, Nachbar [22], I argued that, for a large class of discounted infinitely Repeated Games of complete information (i.e. stage game payoff functions are common knowledge), it is impossible to construct a Bayesian learning theory in which player beliefs are simultaneously weakly cautious, symmetric, and consistent. The present paper establishes a similar impossibility theorem for Repeated Games of incomplete information, that is, for Repeated Games in which stage game payoff functions are private information.
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Non-computable strategies and discounted Repeated Games
Economic Theory, 1996Co-Authors: John H. Nachbar, William R. ZameAbstract:A number of authors have used formal models of computation to capture the idea of “bounded rationality” in Repeated Games. Most of this literature has used computability by a finite automaton as the standard. A conceptual difficulty with this standard is that the decision problem is not “closed.” That is, for every strategy implementable by an automaton, there is some best response implementable by an automaton, but there may not exist any algorithm forfinding such a best response that can be implemented by an automaton. However, such algorithms can always be implemented by a Turing machine, the most powerful formal model of computation. In this paper, we investigate whether the decision problem can be closed by adopting Turing machines as the standard of computability. The answer we offer is negative. Indeed, for a large class of discounted Repeated Games (including the Repeated Prisoner's Dilemma) there exist strategies implementable by a Turing machine for whichno best response is implementable by a Turing machine.
George J. Mailath - One of the best experts on this subject based on the ideXlab platform.
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Reputations in Repeated Games
SSRN Electronic Journal, 2013Co-Authors: George J. Mailath, Larry SamuelsonAbstract:This paper, prepared for the Handbook of Game Theory, Volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in Repeated Games of incomplete information.
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Reputations in Repeated Games, Second Version
SSRN Electronic Journal, 2013Co-Authors: George J. Mailath, Larry SamuelsonAbstract:This paper, prepared for the Handbook of Game Theory, volume 4 (Peyton Young and Shmuel Zamir, editors, Elsevier Press), surveys work on reputations in Repeated Games of incomplete information.
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Repeated Games and Reputations: Long-Run Relationships
2006Co-Authors: George J. Mailath, Larry SamuelsonAbstract:Personalized and continuing relationships play a central role in any society. Economists have built upon the theories of Repeated Games and reputations to make important advances in understanding such relationships. Repeated Games and Reputations begins with a careful development of the fundamental concepts in these theories, including the notions of a Repeated game, strategy, and equilibrium. Mailath and Samuelson then present the classic folk theorem and reputation results for Games of perfect and imperfect public monitoring, with the benefit of the modern analytical tools of decomposability and self-generation. They also present more recent developments, including results beyond folk theorems and recent work in Games of private monitoring and alternative approaches to reputations. Repeated Games and Reputations synthesizes and unifies the vast body of work in this area, bringing the reader to the research frontier. Detailed arguments and proofs are given throughout, interwoven with examples, discussions of how the theory is to be used in the study of relationships, and economic applications. The book will be useful to those doing basic research in the theory of Repeated Games and reputations as well as those using these tools in more applied research. Available in OSO: http://www.oxfordscholarship.com/oso/public/content/economicsfinance/0195300793/toc.html
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Repeated Games and Reputations - Repeated Games and Reputations
2006Co-Authors: George J. Mailath, Larry SamuelsonAbstract:References ABREU, D. (1988): “On the Theory of Infinitely Repeated Games with Discounting,” Econometrica, 56(2), 383–396. ABREU, D., D. PEARCE, AND E. STACCHETTI (1990): “Toward a Theory of Discounted Repeated Games with Imperfect Monitoring,” Econometrica, 58(5), 1041–1063. BHASKAR, V., G. J. MAILATH, AND S. MORRIS (2008): “Purification in the Infinitely-Repeated Prisoners’ Dilemma,” Review of Economic Dynamics, 11(3), 515–528. (2013): “A Foundation for Markov Equilibria in Sequential Games with Finite Social Memory,” Review of Economic Studies, 80(3), 925–948. COLE, H. L., AND N. R. KOCHERLAKOTA (2005): “Finite Memory and Imperfect Monitoring,” Games and Economic Behavior, 53(1), 59–72.
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Repeated Games and reputations
2006Co-Authors: George J. Mailath, Larry SamuelsonAbstract:References ABREU, D. (1988): “On the Theory of Infinitely Repeated Games with Discounting,” Econometrica, 56(2), 383–396. ABREU, D., D. PEARCE, AND E. STACCHETTI (1990): “Toward a Theory of Discounted Repeated Games with Imperfect Monitoring,” Econometrica, 58(5), 1041–1063. BHASKAR, V., G. J. MAILATH, AND S. MORRIS (2008): “Purification in the Infinitely-Repeated Prisoners’ Dilemma,” Review of Economic Dynamics, 11(3), 515–528. (2013): “A Foundation for Markov Equilibria in Sequential Games with Finite Social Memory,” Review of Economic Studies, 80(3), 925–948. COLE, H. L., AND N. R. KOCHERLAKOTA (2005): “Finite Memory and Imperfect Monitoring,” Games and Economic Behavior, 53(1), 59–72.
Guillaume R. Frechette - One of the best experts on this subject based on the ideXlab platform.
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The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence
American Economic Review, 2011Co-Authors: Pedro Dal Bó, Guillaume R. FrechetteAbstract:1 For example, in infinitely Repeated prisoner’s dilemma Games with patient agents, both cooperate and defect may be played in equilibrium. Even though the theory of infinitely Repeated Games has been used to explain cooperation in a variety of environments, no definitive solution has been provided to the problem of equilibrium selection: when both cooperation and defection are possible equilibrium outcomes, which one should we expect to prevail? Previous experimental evidence has shown that subjects often fail to coordinate on a specific equilibrium when they play a small number of infinitely Repeated Games: some subjects attempt to establish cooperative agreements, while others defect. But how would behavior evolve as subjects learn from previous Repeated Games? Would cooperation prevail when it can be supported in equilibrium? Or will subjects learn
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the evolution of cooperation in infinitely Repeated Games experimental evidence
Research Papers in Economics, 2007Co-Authors: Guillaume R. FrechetteAbstract:A usual criticism of the theory of infinitely Repeated Games is that it does not provide sharp predictions since there may be a multiplicity of equilibria. To address this issue, we present experimental evidence on the evolution of cooperation in infinitely Repeated prisoner's dilemma Games as subjects gain experience. We show that cooperation may prevail in infinitely Repeated Games, but the conditions under which this occurs are more stringent than the subgame perfect conditions usually considered or even a condition based on risk dominance. (JEL C71, C73)(This abstract was borrowed from another version of this item.)
Zhu Han - One of the best experts on this subject based on the ideXlab platform.
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Applications of Repeated Games in Wireless Networks: A Survey
arXiv: Computer Science and Game Theory, 2015Co-Authors: Dinh Thai Hoang, Dusit Niyato, Ping Wang, Zhu HanAbstract:A Repeated game is an effective tool to model interactions and conflicts for players aiming to achieve their objectives in a long-term basis. Contrary to static noncooperative Games that model an interaction among players in only one period, in Repeated Games, interactions of players repeat for multiple periods; and thus the players become aware of other players' past behaviors and their future benefits, and will adapt their behavior accordingly. In wireless networks, conflicts among wireless nodes can lead to selfish behaviors, resulting in poor network performances and detrimental individual payoffs. In this paper, we survey the applications of Repeated Games in different wireless networks. The main goal is to demonstrate the use of Repeated Games to encourage wireless nodes to cooperate, thereby improving network performances and avoiding network disruption due to selfish behaviors. Furthermore, various problems in wireless networks and variations of Repeated game models together with the corresponding solutions are discussed in this survey. Finally, we outline some open issues and future research directions.
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Applications of Repeated Games in Wireless Networks: A Survey
IEEE Communications Surveys & Tutorials, 2015Co-Authors: Dinh Thai Hoang, Dusit Niyato, Ping Wang, Dong In Kim, Zhu HanAbstract:A Repeated game is an effective tool to model interactions and conflicts for players aiming to achieve their objectives in a long-term basis. Contrary to static noncooperative Games that model interactions among players in only one period, in Repeated Games, interactions of players repeat for multiple periods. Thus, the players become aware of other players' past behaviors and their future benefits, so as to adapt their strategies accordingly. In wireless networks, conflicts among wireless nodes can lead to selfish behaviors, resulting in poor network performances and detrimental individual payoffs. In this paper, we survey applications of Repeated Games in different wireless networks. The main goal is to demonstrate the use of Repeated Games in encouraging wireless nodes into cooperations, thereby improving network performances and avoiding network disruption due to selfish behaviors. Furthermore, various problems in wireless networks and variations of Repeated game models together with the corresponding solutions are discussed in this survey. Finally, we outline some open issues and future research directions.
