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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

We study repeated games with pure strategies and stochastic discounting under perfect information, with the requirement that the stage game has at least one pure Nash action profile. Players discount future payoffs with a common, but stochastic, discount factor where associated stochastic discounting processes are required to satisfy Markov property, martingale property, having bounded increments, and possessing state spaces with rich ergodic subsets. We, additionally, demand that there are states resulting in discount factors arbitrarily close to 0, and that they are reachable with positive (yet, possibly arbitrarily small) probability in the long run. In this setting, we prove both the perfect Folk Theorem and our main result: The occurrence of any finite number of consecutive repetitions of the period Nash action profile, must almost surely happen within a finite time window no matter which subgame perfect equilibrium strategy is considered and no matter how high the initial discount factor is.

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:17066
Deposited By:Mehmet Barlo
Deposited On:11 Oct 2011 16:38
Last Modified:11 Oct 2011 16:38

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