Barlo, Mehmet and Urgun, Can (2011): Stochastic discounting in repeated games: Awaiting the almost inevitable.
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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:||MPRA Paper|
|Original Title:||Stochastic discounting in repeated games: Awaiting the almost inevitable|
|English Title:||Stochastic discounting in repeated games: Awaiting the almost inevitable|
|Keywords:||Repeated Games; Stochastic Discounting; Stochastic Games; Folk Theorem; Stopping Time|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C79 - Other
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games
|Depositing User:||Mehmet Barlo|
|Date Deposited:||02. Aug 2011 23:16|
|Last Modified:||15. Feb 2013 19:50|
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