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Cycling in a stochastic learning algorithm for normal form games

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  • Martin Posch

    () (Institut f, r Medizinische Statistik der Universit, t Wien, Schwarzspanierstra, e 17, A-1090 Vienna, Austria)

Abstract

In this paper we study a stochastic learning model for 2, 2 normal form games that are played repeatedly. The main emphasis is put on the emergence of cycles. We assume that the players have neither information about the payoff matrix of their opponent nor about their own. At every round each player can only observe his or her action and the payoff he or she receives. We prove that the learning algorithm, which is modeled by an urn scheme proposed by Arthur (1993), leads with positive probability to a cycling of strategy profiles if the game has a mixed Nash equilibrium. In case there are strict Nash equilibria, the learning process converges a.s. to the set of Nash equilibria.

Suggested Citation

  • Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
  • Handle: RePEc:spr:joevec:v:7:y:1997:i:2:p:193-207
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    More about this item

    Keywords

    Evolutionary games ; Learning ; Bounded rationality ; Learning algorithms;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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