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Stochastic Uncoupled Dynamics And Nash Equilibrium

In: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics

Author

Listed:
  • Sergiu Hart
  • Andreu Mas-Colell

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.

Suggested Citation

  • Sergiu Hart & Andreu Mas-Colell, 2013. "Stochastic Uncoupled Dynamics And Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 8, pages 165-189, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814390705_0008
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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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