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Stochastic discounting in repeated games: awaiting the almost inevitable

Ürgün, Can (2011) Stochastic discounting in repeated games: awaiting the almost inevitable. [Thesis]

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Abstract

This thesis 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. We consider stochastic discounting processes satisfying Markov property, Martingale property, having bounded increments (across time) and possessing an infinite state space with a rich ergodic subset. We further require that 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 this study, a player's discount factor is such a process. 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:Thesis
Uncontrolled Keywords:Repeated games. -- Stochastic discounting. -- Stochastic games. -- Folk theorem. -- Stopping time. -- Sonsuz tekrarlı oyunlar. -- Stokastik iskontolama. -- Stokastik oyunlar. -- Folk teoremi. -- Varış zamanı.
Subjects:H Social Sciences > HB Economic Theory
ID Code:19971
Deposited By:IC-Cataloging
Deposited On:01 Nov 2012 11:00
Last Modified:01 Nov 2012 11:00

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