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Learning Efficient Nash Equilibria in Distributed Systems

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  • H Peyton Young
  • Bary S. R. Pradelski

Abstract

An individual's learning rule is completely uncoupled if it does not depend on the actions or payoffs of anyone else. We propose a variant of log linear learning that is completely uncoupled and that selects an efficient pure Nash equilibrium in all generic n-person games that possess at least one pure Nash equilibrium. In games that do not have such an equilibrium, there is a simple formula that expresses the long-run probability of the various disequilibrium states in terms of two factors: i) the sum of payoffs over all agents, and ii) the maximum payoff gain that results from a unilateral deviation by some agent. This welfare/stability trade-off criterion provides a novel framework for analyzing the selection of disequilibrium as well as equilibrium states in n-person games.

Suggested Citation

  • H Peyton Young & Bary S. R. Pradelski, 2010. "Learning Efficient Nash Equilibria in Distributed Systems," Economics Series Working Papers 480, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:480
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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