Instability of Equilibria with Imperfect Private Monitoring

Heller, Yuval (2015): Instability of Equilibria with Imperfect Private Monitoring.

Abstract

Various papers have presented folk-theorem results that yield efficiency in the repeated Prisoner's Dilemma with imperfect private monitoring. I present a mild equilibrium refinement that requires robustness against small perturbations in the behavior of potential opponents, and I show that only defection satisfies this mild refinement among all the equilibria in the existing literature, unless one assumes either (1) communication among the players, or (2) sufficient correlation between the private signals (conditional on the action-profile).

• Item Type: MPRA Paper
• Language: English
• Keywords: Belief-free equilibrium, evolutionary stability, imperfect private monitoring, repeated Prisoner's Dilemma, communication.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D82 - Asymmetric and Private Information ; Mechanism Design

References

Abreu, Dilip, Pearce, David, & Stacchetti, Ennio. 1990. Toward a theory of discounted repeated games with imperfect monitoring. Econometrica: Journal of the Econometric Society, 1041–1063.

Benaïm, Michel, Hofbauer, Josef, & Hopkins, Ed. 2009. Learning in games with unstable equilibria. Journal of Economic Theory, 144(4), 1694–1709.

Bhaskar, V. 2000. The robustness of repeated game equilibria to incomplete payoff information, University of Essex.

Bhaskar, V, & Obara, Ichiro. 2002. Belief-based equilibria in the repeated prisoners’ dilemma with private monitoring. Journal of Economic Theory, 102(1), 40–69.

Bhaskar, V, Mailath, George J, & Morris, Stephen. 2008. Purification in the infinitely-repeated prisoners’ dilemma. Review of Economic Dynamics, 11(3), 515–528.

Compte, Olivier. 1998. Communication in repeated games with imperfect private monitoring. Econometrica, 597–626.

Ely, Jeffrey C, & Välimäki, Juuso. 2002. A robust folk theorem for the prisoner’s dilemma. Journal of Economic Theory, 102(1), 84–105.

Ely, Jeffrey C, Hörner, Johannes, & Olszewski, Wojciech. 2005. Belief-free equilibria in repeated games. Econometrica, 73(2), 377–415.

Fudenberg, Drew, & Maskin, Eric. 1986. The folk theorem in repeated games with discounting or with incomplete information. Econometrica: Journal of the Econometric Society, 533–554.

Heller, Yuval, & Mohlin, Erik. 2015. Stable Observable Behavior. Unpublished.

Hörner, Johannes, & Olszewski, Wojciech. 2006. The Folk Theorem for Games with Private Almost-Perfect Monitoring. Econometrica, 74(6), 1499–1544.

Kandori, Michihiro. 2002. Introduction to repeated games with private monitoring. Journal of Economic Theory, 102(1), 1–15.

Kandori, Michihiro. 2011. Weakly Belief-Free Equilibria in Repeated Games With Private Monitoring. Econometrica, 79(3), 877–892.

Kandori, Michihiro, & Matsushima, Hitoshi. 1998. Private observation, communication and collusion. Econometrica, 627–652.

Kandori, Michihiro, & Obara, Ichiro. 2006. Efficiency in repeated games revisited: The role of private strategies. Econometrica, 74(2), 499–519.

Mailath, George J, & Morris, Stephen. 2002. Repeated games with almost-public monitoring. Journal of Economic Theory, 102(1), 189–228.

Mailath, George J, & Morris, Stephen. 2006. Coordination failure in repeated games with almost-public monitoring. Theoretical Economics, 1(3), 311–340.

Mailath, George J, & Samuelson, Larry. 2006. Repeated games and reputations. Vol. 2. Oxford university press Oxford.

Matsushima, Hitoshi. 2004. Repeated games with private monitoring: Two players. Econometrica, 72(3), 823–852.

Maynard-Smith, John. 1982. Evolution and the theory of games. Cambridge University Press. Maynard Smith, John, & Price, George R. 1973. The logic of animal conflict. Nature, 246, 15.

Miyagawa, Eiichi, Miyahara, Yasuyuki, & Sekiguchi, Takashi. 2008. The folk theorem for repeated games with observation costs. Journal of Economic Theory, 139(1), 192–221.

Obara, Ichiro. 2009. Folk theorem with communication. Journal of Economic Theory, 144(1), 120–134.

Piccione, Michele. 2002. The repeated prisoner’s dilemma with imperfect private monitoring. Journal of Economic Theory, 102(1), 70–83.

Sekiguchi, Tadashi. 1997. Efficiency in repeated prisoner’s dilemma with private monitoring. Journal of Economic Theory, 76(2), 345–361.

Sugaya, Takuo, & Takahashi, Satoru. 2013. Coordination failure in repeated games with private monitoring. Journal of Economic Theory, 148(5), 1891–1928.

Takahashi, Satoru. 2010. Community enforcement when players observe partners’ past play. Journal of Economic Theory, 145(1), 42–62.

Weibull, Jörgen W. 1995. Evolutionary game theory. The MIT press.

Yamamoto, Yuichi. 2007. Efficiency results in N player games with imperfect private monitoring. Journal of Economic Theory, 135(1), 382–413.

Yamamoto, Yuichi. 2009. A limit characterization of belief-free equilibrium payoffs in repeated games. Journal of Economic Theory, 144(2), 802–824.

Yamamoto, Yuichi. 2012. Characterizing belief-free review-strategy equilibrium payoffs under conditional independence. Journal of Economic Theory, 147(5), 1998–2027.

Yamamoto, Yuichi. 2013. Individual learning and cooperation in noisy repeated games. The Review of Economic Studies.