Stochastic uncoupled dynamics and Nash equilibrium |
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Authors: | Sergiu Hart Andreu Mas-Colell |
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Affiliation: | aCenter for the Study of Rationality, Institute of Mathematics, and Department of Economics, The Hebrew University of Jerusalem, Feldman Building, Givat Ram, 91904 Jerusalem, Israel;bDepartment of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain |
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Abstract: | In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence of play (the period-by-period behavior as well as the long-run frequency) to Nash equilibria of the one-shot stage game, and present a number of possibility and impossibility results. Basically, we show that if in addition to random experimentation some recall, or memory, is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it suffices to recall the last two periods of play. |
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Keywords: | Uncoupled Nash equilibrium Stochastic dynamics Finite recall Finite memory Finite automaton Exhaustive experimentation |
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