Private Strategies in Finitely Repeated Games with Imperfect Public Monitoring

2002 ◽  
Vol 2 (1) ◽  
Author(s):  
George J. Mailath ◽  
Steven A. Matthews ◽  
Tadashi Sekiguchi
Keyword(s):  
Nash Equilibrium ◽  
Repeated Games ◽  
Finitely Repeated Games ◽  
Game Equilibrium ◽  
Public Signals ◽  
Stage Game ◽  
Public Monitoring ◽  
Public Signal ◽  
Action Profile

We present three examples of finitely repeated games with public monitoring that have sequential equilibria in private strategies, i.e., strategies that depend on own past actions as well as public signals. Such private sequential equilibria can have features quite unlike those of the more familiar perfect public equilibria: (i) making a public signal less informative can create Pareto superior equilibrium outcomes; (ii) the equilibrium final-period action profile need not be a stage game equilibrium; and (iii) even if the stage game has a unique correlated (and hence Nash) equilibrium, the first-period action profile need not be a stage game equilibrium.

scholarly journals The Impact of Monitoring in Infinitely Repeated Games: Perfect, Public, and Private

2019 ◽  
Vol 11 (1) ◽  
pp. 1-43 ◽  
Author(s):  
Masaki Aoyagi ◽  
V. Bhaskar ◽  
Guillaume R. Fréchette
Keyword(s):  
Laboratory Experiment ◽  
Repeated Games ◽  
Imperfect Monitoring ◽  
Public And Private ◽  
Private Monitoring ◽  
Stage Game ◽  
The Impact ◽  
Public Monitoring ◽  
Perfect Monitoring ◽  
Infinitely Repeated Games

This paper uses a laboratory experiment to study the effect of the monitoring structure on the play of the infinitely repeated prisoner’s dilemma. Keeping the strategic form of the stage game fixed, we examine the behavior of subjects when information about past actions is perfect (perfect monitoring), noisy but public (public monitoring), and noisy and private (private monitoring). We find that the subjects sustain cooperation in every treatment, but that their strategies differ across the three treatments. Specifically, the strategies under imperfect monitoring are both more complex and more lenient than those under perfect monitoring. The results show how the changes in strategies across monitoring structures mitigate the effect of noise in monitoring on efficiency. (JEL C72, C73, C92, D82, D83)

scholarly journals Reactive Strategies: An Inch of Memory, a Mile of Equilibria

Games ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 42
Author(s):  
Artem Baklanov
Keyword(s):  
Nash Equilibrium ◽  
Repeated Games ◽  
Folk Theorem ◽  
Pareto Improvement ◽  
Symmetric Equilibrium ◽  
Equilibrium Payoff ◽  
Incremental Change ◽  
Symmetric Games ◽  
Stage Game

We explore how an incremental change in complexity of strategies (“an inch of memory”) in repeated interactions influences the sets of Nash Equilibrium (NE) strategy and payoff profiles. For this, we introduce the two most basic setups of repeated games, where players are allowed to use only reactive strategies for which a probability of players’ actions depends only on the opponent’s preceding move. The first game is trivial and inherits equilibria of the stage game since players have only unconditional (memory-less) Reactive Strategies (RSs); in the second one, players also have conditional stochastic RSs. This extension of the strategy sets can be understood as a result of evolution or learning that increases the complexity of strategies. For the game with conditional RSs, we characterize all possible NE profiles in stochastic RSs and find all possible symmetric games admitting these equilibria. By setting the unconditional benchmark as the least symmetric equilibrium payoff profile in memory-less RSs, we demonstrate that for most classes of symmetric stage games, infinitely many equilibria in conditional stochastic RSs (“a mile of equilibria”) Pareto dominate the benchmark. Since there is no folk theorem for RSs, Pareto improvement over the benchmark is the best one can gain with an inch of memory.

Strategic absentmindedness in finitely repeated games

Top ◽  
2009 ◽  
Vol 17 (1) ◽  
pp. 85-95
Author(s):  
Ignacio García-Jurado ◽  
Natividad Llorca ◽  
Ana Meca ◽  
Manuel A. Pulido ◽  
Joaquín Sánchez-Soriano
Keyword(s):  
Repeated Games ◽  
Finitely Repeated Games

Stability Analysis of Supply Chain Cooperation Contract under Asymmetric Information

2010 ◽  
Vol 44-47 ◽  
pp. 794-798 ◽  
Author(s):  
Xin Ma
Keyword(s):  
Game Theory ◽  
Supply Chain ◽  
Repeated Games ◽  
Information Structure ◽  
Transition Period ◽  
Information Economics ◽  
Real Life ◽  
The Other ◽  
Game Equilibrium ◽  
The Stability

The stability of cooperation contract is the result of abandon opportunistic behavior in the process of repeated games among the enterprise and the other subjects in the supply chain from long-term interests, and is also the foundation of healthy development for the whole supply chain. But in real life cooperation contract instability everywhere for a variety of reasons, such as ethical considerations, institutional factors, cultural factors and special reasons during the transition period and so on. From the perspective of information economics and game theory, the main game process of cooperation between enterprise and the other subjects in supply chain is not only the game of information, but also the game of interests. Information structure and the interesting structure are the important factors for the subjects of the game of the implementation of decisions and the basic contractual constraints for cooperative game equilibrium. Cooperation behaviors among the enterprise and the other subjects in the supply chain were studied on the basis of game theory, and the stability of cooperation contract is also being discussed in this paper.

scholarly journals Cooperation between Emotional Players

Games ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 45
Author(s):  
Lina Andersson
Keyword(s):  
Repeated Games ◽  
Stochastic Games ◽  
The State ◽  
The Other ◽  
States Of Mind ◽  
Finitely Repeated Games ◽  
Prisoners Dilemma ◽  
State Of Mind ◽  
Infinitely Repeated Games

This paper uses the framework of stochastic games to propose a model of emotions in repeated interactions. An emotional player can be in either a friendly, a neutral, or a hostile state of mind. The player transitions between the states of mind as a response to observed actions taken by the other player. The state of mind determines the player’s psychological payoff which together with a material payoff constitutes the player’s utility. In the friendly (hostile) state of mind the player has a positive (negative) concern for other players’ material payoffs. This paper shows how emotions can both facilitate and obstruct cooperation in a repeated prisoners’ dilemma game. In finitely repeated games a player who cares only for their own material payoffs can have an incentive to manipulate an emotional player into the friendly state of mind. In infinitely repeated games with two emotional players less patience is required to sustain cooperation. However, emotions can also obstruct cooperation if they make the players unwilling to punish each other, or if the players become hostile when punished.

scholarly journals Group Reputations, Stereotypes, and Cooperation in a Repeated Labor Market

2007 ◽  
Vol 97 (5) ◽  
pp. 1751-1773 ◽  
Author(s):  
Paul J Healy
Keyword(s):  
Labor Market ◽  
Moral Hazard ◽  
Infinite Time ◽  
Time Horizons ◽  
Game Equilibrium ◽  
Finite Horizons ◽  
Stage Game ◽  
Reputation Effects ◽  
Other Regarding ◽  
Other Regarding Preferences

Reputation effects and other-regarding preferences have both been used to predict cooperative outcomes in markets with inefficient equilibria. Existing reputationbuilding models require either infinite time horizons or publicly observed identities, but cooperative outcomes have been observed in several moral hazard experiments with finite horizons and anonymous interactions. This paper introduces a full reputation equilibrium (FRE) with stereotyping (perceived type correlation) in which cooperation is predicted in early periods of a finitely repeated market with anonymous interactions. New experiments generate results in line with the FRE prediction, including final-period reversions to stage-game equilibrium and noncooperative play under unfavorable payoff parameters. (JEL C72, C73, C78, J41)

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