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Stochastic discounting in repeated games: awaiting the almost inevitable

Barlo, Mehmet and Ürgün, Can (2011) Stochastic discounting in repeated games: awaiting the almost inevitable. [Working Paper / Technical Report] Sabanci University ID:SU_FASS_2011/0001

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Abstract

This paper studies repeated games with pure strategies and stochastic discounting under perfect information. We consider infinite repetitions of any finite normal form game possessing at least one pure Nash action profile. The period interaction realizes a shock in each period, and the cumulative shocks while not affecting period returns, determine the probability of the continuation of the game. We require cumulative shocks to satisfy the following: (1) Markov property; (2) to have a non-negative (across time) covariance matrix; (3) to have bounded increments (across time) and possess a denumerable state space with a rich ergodic subset; (4) there are states of the stochastic process with the resulting stochastic discount factor arbitrarily close to 0, and such states can be reached with positive (yet possibly arbitrarily small) probability in the long run. In our study, a player’s discount factor is a mapping from the state space to (0, 1) satisfying the martingale property. In this setting, we, not only establish the (subgame perfect) folk theorem, but also prove the main result of this study: In any equilibrium path, the occurrence of any finite number of consecutive repetitions of the period Nash action profile, must almost surely happen within a finite time window. That is, any equilibrium strategy almost surely contains arbitrary long realizations of consecutive period Nash action profiles.

Item Type:Working Paper / Technical Report
Uncontrolled Keywords:Repeated Games; Stochastic Discounting; Stochastic Games; Folk Theorem; Stopping Time
Subjects:H Social Sciences > HB Economic Theory > HB135-147 Mathematical economics. Quantitative methods
ID Code:16342
Deposited By:Mehmet Barlo
Deposited On:03 Feb 2011 12:28
Last Modified:11 Oct 2011 16:38

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