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Wojciech Olszewski - One of the best experts on this subject based on the ideXlab platform.
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How Robust is the Folk Theorem
Quarterly Journal of Economics, 2009Co-Authors: Johannes Hörner, Wojciech OlszewskiAbstract:The Folk Theorem of repeated games has established that cooperative behavior can be sustained as an equilibrium in repeated settings. Early papers on private monitoring and a recent paper of Cole and Kocherlakota (Games and Economic Behavior, 53 [2005], 59–72) challenge the robustness of this result by providing examples in which cooperation breaks down when players observe only imperfect private signals about other players' actions, or when attention is restricted to strategies with finite memory. This paper shows that Cole and Kocherlakota's result is an artefact of a further restriction that they impose. We prove that the Folk Theorem with imperfect public monitoring holds with strategies with finite memory. As a corollary, we establish that the Folk Theorem extends to environments in which monitoring is close to public, yet private.
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Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring, Second Version
2008Co-Authors: George J. Mailath, Wojciech OlszewskiAbstract:We prove the perfect-monitoring Folk Theorem continues to hold when attention is restricted to strategies with bounded recall and the equilibrium is essentially required to be strict. As a consequence, the perfect monitoring Folk Theorem is shown to be behaviorally robust under almost-perfect almost-public monitoring. That is, the same specification of behavior continues to be an equilibrium when the monitoring is perturbed from perfect to highly-correlated private.
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The Folk Theorem for Games with Private Almost‐Perfect Monitoring
Econometrica, 2006Co-Authors: Johannes Hörner, Wojciech OlszewskiAbstract:We prove the Folk Theorem for discounted repeated games under private, almost-perfect monitoring. Our result covers all finite, n-player games that satisfy the usual full-dimensionality condition. Mixed strategies are allowed in determining the individually rational payoffs. We assume no cheap-talk communication between players and no public randomization device.
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The Folk Theorem for games with private almost-perfect monitoring
2005Co-Authors: Johannes Hörner, Wojciech OlszewskiAbstract:We prove the Folk Theorem for discounted repeated games under private, almost-perfect monitoring. Our result covers all finite, n-player games that satisfy the usual full-dimensionality condition. Mixed strategies are allowed in determining the individually rational payoffs. We assume no cheap-talk communication between players and no public randomization device.
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The Folk Theorem for all games with almost perfect monitoring
2004Co-Authors: Wojciech Olszewski, Johannes HörnerAbstract:"Selection in Dynamic Games" 1. Assortative Matching with costly search, presented by Alp Atakan 2. A Refinement of Sequential Equilibrium with Application to Decentralized Collusion, presented by Peter Eso 3. Noisy evolution in Normal form Games, presented by Christoph Kuzmics 4. The Folk Theorem for all games with almost perfect monitoring presented by Johannes Horner Abstract: We study repeated games in which monitoring is imperfect and private. We prove the Folk Theorem for all two-player (finite) games assuming that the monitoring is almost perfect, but not necessarily almost public
Johannes Hörner - One of the best experts on this subject based on the ideXlab platform.
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Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem
Econometrica, 2011Co-Authors: Nicolas Vieille, Johannes Hörner, Takuo Sugaya, Satoru TakahashiAbstract:We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to 1 for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a Folk Theorem obtains: if in each state the joint distribution over the public signal and next period's state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.
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recursive methods in discounted stochastic games an algorithm for δ 1 and a Folk Theorem
2010Co-Authors: Johannes Hörner, Satoru Takahashi, Takuo Sugaya, Nicolas VieilleAbstract:We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players’) equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a Folk Theorem obtains: if in each state the joint distribution over the public signal and next period’s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.
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recursive methods in discounted stochastic games an algorithm for delta approaching 1 and a Folk Theorem
2010Co-Authors: Johannes Hörner, Satoru Takahashi, Takuo Sugaya, Nicolas VieilleAbstract:We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a Folk Theorem obtains: if in each state the joint distribution over the public signal and next period’s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.
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Recursive Methods in Discounted Stochastic Games: An Algorithm for ! ! 1 and a Folk Theorem
2010Co-Authors: Nicolas Vieille, Johannes Hörner, Takuo Sugaya, Satoru TakahashiAbstract:We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players?) equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a Folk Theorem obtains: if in each state the joint distribution over the public signal and next period?s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.
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recursive methods in discounted stochastic games an algorithm for 1 and a Folk Theorem
Post-Print, 2010Co-Authors: Nicolas Vieille, Johannes Hörner, Takuo Sugaya, Satoru TakahashiAbstract:We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players?) equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a Folk Theorem obtains: if in each state the joint distribution over the public signal and next period?s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.
Takuo Sugaya - One of the best experts on this subject based on the ideXlab platform.
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a few bad apples spoil the barrel an anti Folk Theorem for anonymous repeated games with incomplete information
The American Economic Review, 2020Co-Authors: Takuo Sugaya, Alexander WolitzkyAbstract:We study anonymous repeated games where players may be "commitment types" who always take the same action. We establish a stark anti-Folk Theorem: if the distribution of the number of commitment types satisfies a smoothness condition and the game has a "pairwise dominant" action, this action is almost always taken. This implies that cooperation is impossible in the repeated prisoner's dilemma with anonymous random matching. We also bound equilibrium payoffs for general games. Our bound implies that industry profits converge to zero in linear-demand Cournot oligopoly as the number of firms increases.
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The Folk Theorem in Repeated Games With Anonymous Random Matching
Econometrica, 2020Co-Authors: Joyee Deb, Takuo Sugaya, Alexander WolitzkyAbstract:We prove the Folk Theorem for discounted repeated games with anonymous random matching. We allow non‐uniform matching, include asymmetric payoffs, and place no restrictions on the stage game other than full dimensionality. No record‐keeping or communication devices—including cheap talk communication and public randomization—are necessary.
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The Nash-Threat Folk Theorem in Repeated Games with Private Monitoring and Public Communication
2012Co-Authors: Takuo SugayaAbstract:Assuming that cheap talk is available, we show that the Nash-threat Folk Theorem holds for repeated games with private monitoring if the individual full rank condition is satis…ed.
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Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem
Econometrica, 2011Co-Authors: Nicolas Vieille, Johannes Hörner, Takuo Sugaya, Satoru TakahashiAbstract:We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to 1 for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a Folk Theorem obtains: if in each state the joint distribution over the public signal and next period's state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.
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The Folk Theorem in repeated games with private monitoring
SSRN Electronic Journal, 2011Co-Authors: Takuo SugayaAbstract:We show that the Folk Theorem with individually rational payoffs defined by pure strategies generically holds for a general N-player repeated game with private monitoring when the number of each player’s signals is sufficiently large. No cheap talk communication device or public randomization device is necessary.
Roger Lagunoff - One of the best experts on this subject based on the ideXlab platform.
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An "Anti-Folk Theorem " for a Class of Asynchronously
2015Co-Authors: Repeated Games, Roger Lagunoff, Akihiko Matsui, Akihiko MatsuitAbstract:It is well known from the Folk Theorem that infinitely repeated games admit a multitude of equilibria. This paper demonstrates that in some types of games, the Folk Theorem form of multiplicity is an artifact of the standard representation which assumes perfect synchronization in the timing of actions between the players. We define here a more general family of repeated settings called renewal games. Specifically, a renewal game is a setting in which a stage game is repeated in continuous time, and at certain stochastic points in time determined by an arbitrary renewal process some set of players may be called upon to make a move. A stationary, ergodic Markov process determines who moves at each decision node. We restrict attention in this paper to a natural subclass of renewal games called asynchronously repeated games, in which no two individuals can change their actions simultaneously. Special cases include the alternating move game, and the Poisson revision game. In the latter, each player adjusts his action independently at Poisson distributed times. Our main result concerns asynchronously repeated games of pure coordination (where the pay offs of all players in the stage game are identical up to an affine transformation): given €> 0, i
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A “Super” Folk Theorem for dynastic repeated games
Economic Theory, 2008Co-Authors: Luca Anderlini, Dino Gerardi, Roger LagunoffAbstract:We analyze dynastic repeated games . These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n ≥ 4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.”
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A "Super" Folk Theorem for dynastic repeated games
Economic Theory, 2007Co-Authors: Luca Anderlini, Dino Gerardi, Roger LagunoffAbstract:We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are suciently patient, all feasible payo vec- tors (including those below the minmax of the stage game) can be sustained by Sequen- tial Equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n 4 players for which the standard Folk Theorem yields a payo set with a non-empty interior.
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a super Folk Theorem in dynastic repeated games
Levine's Bibliography, 2007Co-Authors: Luca Anderlini, Dino Gerardi, Roger LagunoffAbstract:We analyze "dynastic" repeated games. A stage game is repeatedly played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. When all players observe the past history of play, the standard repeated game and the dynastic game are equivalent In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors. Under very mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize entirely when a Sequential Equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a Subgame Perfect Equilibrium of the standard repeated game. For this to be the case it must be that the players' equilibrium beliefs violate a condition that we term "Inter-Generational Agreement." (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.) (This (This abstract was borrowed from another version of this item.)
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a super Folk Theorem for dynastic repeated games
2006Co-Authors: Luca Anderlini, Dino Gerardi, Roger LagunoffAbstract:We analyze "dynastic" repeated games. A stage game is repeatedly played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. When all players observe the past history of play, the standard repeated game and the dynastic game are equivalent In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors. Under very mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize entirely when a Sequential Equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a Subgame Perfect Equilibrium of the standard repeated game. For this to be the case it must be that the players' equilibrium beliefs violate a condition that we term "Inter-Generational Agreement."
Juuso Välimäki - One of the best experts on this subject based on the ideXlab platform.
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A Robust Folk Theorem for the Prisoner's Dilemma☆
Journal of Economic Theory, 2002Co-Authors: Jeffrey C. Ely, Juuso VälimäkiAbstract:We prove the Folk Theorem for the Prisoner's dilemma using strategies that are robust to private monitoring. From this follows a limit Folk Theorem: when players are patient and monitoring is sufficiently accurate, (but private and possibly independent) any feasible individually rational payoff can be obtained in sequential equilibrium. The strategies used can be implemented by finite (randomizing) automata. Journal of Economic Literature Classification Numbers: C72, C73, D82.