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23
Subjective Games And Equilibria
, 1994
"... Applying the concepts of Nash, Bayesian, and correlated equilibrium to analysis of strategic interaction, requires that players possess objective knowledge of the game and opponents' strategies. Such knowledge is often not available. The proposed notions of subjective games, and subjective Nash ..."
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Cited by 26 (1 self)
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Applying the concepts of Nash, Bayesian, and correlated equilibrium to analysis of strategic interaction, requires that players possess objective knowledge of the game and opponents' strategies. Such knowledge is often not available. The proposed notions of subjective games, and subjective Nash and correlated equilibria, replace essential unavailable objective knowledge by subjective assessments. When playing a subjective game repeatedly, subjective optimizers converge to a subjective equilibrium. We apply this approach to some well known examples including a single multiarm bandit player, multiperson multiarm bandit games, and repeated Cournot oligopoly games.
Comparison of information structures
 Games Econ. Behav
, 2000
"... We introduce two ways of comparing information structures, say I and J. First we say that I is richer than J when for every compact game G, all correlated equilibrium distributions of G induced by J are also induced by I. Second, we say that J is faithfully reproducable from I when all the players c ..."
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Cited by 10 (2 self)
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We introduce two ways of comparing information structures, say I and J. First we say that I is richer than J when for every compact game G, all correlated equilibrium distributions of G induced by J are also induced by I. Second, we say that J is faithfully reproducable from I when all the players can compute from their information in I “new information ” that they could have received from J. We prove that I is richer than J if and only if J is faithfully reproducable from I.
The folk theorem for repeated games with observation costs
 J. Econ. Theory
, 2008
"... The folk theorem literature has been relaxing the assumption on how much players know about each other’s past action. Here we consider a general model where players can “buy ” precise information. Every period, each player decides whether to pay a cost to accurately observe the actions chosen by oth ..."
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Cited by 9 (2 self)
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The folk theorem literature has been relaxing the assumption on how much players know about each other’s past action. Here we consider a general model where players can “buy ” precise information. Every period, each player decides whether to pay a cost to accurately observe the actions chosen by other players in the previous period. When a player does not pay the cost, he obtains only imperfect private signals. Observational decisions are unobservable to others. Known strategies such as trigger strategies do not work since they fail to motivate players to pay for information. This paper shows that the folk theorem holds for any level of observation costs. Unlike existing folk theorems with private monitoring, ours imposes virtually no restriction on the nature of costless imperfect signals. The theorem does not use explicit or costless communication, thereby having implications on antitrust laws that rely on evidence of explicit communication. The main message is that accurate observation alone, however costly, enables efficient cooperation in general repeated games.
Repeated Communication through the and Mechanism
 International Journal of Game Theory
, 2001
"... We consider the “and ” communication device that receives inputs from two players and outputs the public signal yes if both messages are yes, and outputs no otherwise. We prove that no correlation can securely be implemented using this device, even when infinitely many stages of communication are al ..."
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Cited by 8 (1 self)
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We consider the “and ” communication device that receives inputs from two players and outputs the public signal yes if both messages are yes, and outputs no otherwise. We prove that no correlation can securely be implemented using this device, even when infinitely many stages of communication are allowed.
Secret correlation in repeated games with imperfect monitoring
 MATHEMATICS OF OPERATION RESEARCH
, 2007
"... We characterize the maximum payoff that a team can guarantee against another in a class of repeated games with imperfect monitoring. Our result relies on the optimal tradeoff for the team between optimization of stagepayoffs and generation of signals for future correlation. ..."
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Cited by 6 (2 self)
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We characterize the maximum payoff that a team can guarantee against another in a class of repeated games with imperfect monitoring. Our result relies on the optimal tradeoff for the team between optimization of stagepayoffs and generation of signals for future correlation.
Adaptive Learning in Imperfect Monitoring Games
 Review of Economic Dynamics
, 1999
"... This paper deals with the problem of specifying a general learning model, the rationality of which is not situation dependent. I propose a very general model of adaptive learning suitable to study learning problems in games with imperfect monitoring, such as extensive form games. In this context I r ..."
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Cited by 4 (1 self)
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This paper deals with the problem of specifying a general learning model, the rationality of which is not situation dependent. I propose a very general model of adaptive learning suitable to study learning problems in games with imperfect monitoring, such as extensive form games. In this context I relate adaptive learning with a general notion of equilibrium. In particular I provide a dynamic haractedsation of.conjectural equilibria: a "stable " strategy profile is consistent with adaptive learning if and only if it is a conjectural equilibrium. Journal of Economic
Perfect communication equilibria in repeated games with imperfect monitoring
, 2007
"... This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a selection of Myerson’s ([25]) communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of t ..."
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Cited by 4 (0 self)
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This paper introduces an equilibrium concept called perfect communication equilibrium for repeated games with imperfect private monitoring. This concept is a selection of Myerson’s ([25]) communication equilibrium. A communication equilibrium is perfect if it induces a communication equilibrium of the continuation game, after every history of messages of the mediator. We provide a characterization of the set of corresponding equilibrium payoffs and derive a Folk Theorem for discounted repeated games with imperfect private monitoring.
Learning the State of Nature in Repeated Games With Incomplete Information and Signals
"... The motivation of this paper comes from repeated games with incomplete information and imperfect monitoring. We saythatanequilibriumiscompletelyrevealingifitallows each playertolearnthestateofnature.Our aim istodescribe thecomm unication structuresforwhich such an equilibriumexistsfor any payofi fun ..."
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Cited by 3 (2 self)
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The motivation of this paper comes from repeated games with incomplete information and imperfect monitoring. We saythatanequilibriumiscompletelyrevealingifitallows each playertolearnthestateofnature.Our aim istodescribe thecomm unication structuresforwhich such an equilibriumexistsfor any payofi function.W e consider thus an interactioninwhich players,facingsome incompleteinformationaboutthe stateofnature,exchangemessageswhileimperfectlymonitoring them.W e thenask thequestion:canplayerslearnthetruestate even underunilateraldeviations? W e giveananswerby defining learning functions which describe what a player can learn by communicatingrepeatedlythroughtheimperfectmonitoring structure. To get effective learninginequilibrium, werequirethosefunctionstopossess properties of robustness to unilateral deviations. We compute these functions explicitly for particular monitoring structures.
Entropy and codification in repeated games with imperfect monitoring, DP 2003/33
 in Game Theory and Applications, edited by
, 2003
"... Abstract. We characterize the minmax values of a class of repeated games with imperfect monitoring. Our result relies on the optimal tradeoff for the team formed by punishing players between optimization of stagepayoffs and generation of signals for future correlation. Amounts of correlation are ..."
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Abstract. We characterize the minmax values of a class of repeated games with imperfect monitoring. Our result relies on the optimal tradeoff for the team formed by punishing players between optimization of stagepayoffs and generation of signals for future correlation. Amounts of correlation are measured through the entropy function. Our theorem on minmax values stems from a more general characterization of optimal strategies for a class of optimization problems. 1.
REPEATED GAMES WITH PARTIAL MONITORING: THE STOCHASTIC SIGNALING CASE
"... ABSTRACT. In this work we extend a result of Lehrer characterizing the correlated equilibrium payoffs in undiscounted two player repeated games with partial monitoring to the case in which the signals are permitted to be stochastic. In particular we develop appropriate versions of Lehrer’s concepts ..."
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ABSTRACT. In this work we extend a result of Lehrer characterizing the correlated equilibrium payoffs in undiscounted two player repeated games with partial monitoring to the case in which the signals are permitted to be stochastic. In particular we develop appropriate versions of Lehrer’s concepts of “indistinguishable ” and “more informative. ” We also show that any payoff associated with a (correlated) distribution on strategy vectors in the stage game such that neither player can profitably deviate from one of his strategies to another that is indistinguishable and more informative is the payoff of a correlated equilibrium of the