Randomization, Communication, and Efficiency in Repeated Games with Imperfect Public Monitoring

Econometrica ◽  
2003 ◽  
Vol 71 (1) ◽  
pp. 345-353 ◽  
Author(s):  
Kandori Michihiro
Keyword(s):  
Repeated Games ◽  
Public Monitoring

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.

The Folk Theorem for Repeated Games with Time-Dependent Discounting

2021 ◽  
Author(s):  
Daehyun Kim ◽  
Xiaoxi Li
Keyword(s):  
Repeated Games ◽  
Folk Theorem ◽  
The Self ◽  
Time Dependent ◽  
Constructive Proof ◽  
The Public ◽  
Discount Factors ◽  
Time Inconsistent ◽  
Public Monitoring ◽  
Perfect Monitoring

This paper defines a general framework to study infinitely repeated games with time-dependent discounting in which we distinguish and discuss both time-consistent and -inconsistent preferences. To study the long-term properties of repeated games, we introduce an asymptotic condition to characterize the fact that players become more and more patient; that is, the discount factors at all stages uniformly converge to one. Two types of folk theorems are proven without the public randomization assumption: the asymptotic one, that is, the equilibrium payoff set converges to the feasible and individual rational set as players become patient, and the uniform one, that is, any payoff in the feasible and individual rational set is sustained by a single strategy profile that is an approximate subgame perfect Nash equilibrium in all games with sufficiently patient discount factors. We use two methods for the study of asymptotic folk theorem: the self-generating approach and the constructive proof. We present the constructive proof in the perfect-monitoring case and show that it can be extended to time-inconsistent preferences. The self-generating approach applies to the public-monitoring case but may not extend to time-inconsistent preferences because of a nonmonotonicity result.

scholarly journals Repeated Games with Almost-Public Monitoring

2002 ◽  
Vol 102 (1) ◽  
pp. 189-228 ◽  
Author(s):  
George J. Mailath ◽  
Stephen Morris
Keyword(s):  
Repeated Games ◽  
Public Monitoring

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)

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