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Stationarity and Chaos in Infinitely Repeated Games of Incomplete Information

McKelvey, Richard D. and Palfrey, Thomas R. (1992) Stationarity and Chaos in Infinitely Repeated Games of Incomplete Information. Social Science Working Paper, 803. California Institute of Technology , Pasadena, CA. (Unpublished)

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Consider an incomplete information game in which the players first learn their own types, and then infinitely often play the same normal form game with the same opponents. After each play, the players observe their own payoff and the action of their opponents. The payoff for a strategy n-tuple in the infinitely repeated game is the discounted present value of the infinite stream of payoffs generated by the strategy. This paper studies Bayesian learning in such a setting. Kalai and Lehrer [1991] and Jordan [1991] have shown that Bayesian equilibria to such games exist and eventually look like Nash equilibria to the infinitely repeated full information game with the correct types. However, due to folk theorems for complete information games, this still leaves the class of equilibria for such games to be quite large. In order to refine the set of equilibria, we impose a restriction on the equilibrium strategies of the players which requires stationarity with respect to the profile of current beliefs: if the same profile of beliefs is reached at two different points in time, the players must choose the same behavioral strategy at both points in time. This set, called the belief stationary equilibria, is a subset of the Bayesian Nash equilibria. We compute a belief stationary equilibrium in an example. The equilibria that result can have elements of chaotic behavior. The equilibrium path of beliefs when types are not revealed can be chaotic, and small changes in initial beliefs can result in large changes in equilibrium actions.

Item Type:Report or Paper (Working Paper)
Palfrey, Thomas R.0000-0003-0769-8109
Additional Information:This is a revision of a paper that was previously titled "Belief Stationary Equilibria to Infinitely Repeated Games of Incomplete Information." This research was supported, in part by NSF grant #SES-9011828 to the California Institute of Technology. We thank Tim Fedderson for helpful comments.
Group:Social Science Working Papers
Funding AgencyGrant Number
Series Name:Social Science Working Paper
Issue or Number:803
Record Number:CaltechAUTHORS:20170829-135834135
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80911
Deposited By: Jacquelyn Bussone
Deposited On:30 Aug 2017 17:49
Last Modified:22 Nov 2019 09:58

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