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Stochastic Adaptation in Finite Games Played by Heterogeneous Populations

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  • Josephson, Jens

    ()
    (Dept. of Economics, Stockholm School of Economics)

Abstract

In this paper, I analyze stochastic adaptation in finite n-player games played by heterogeneous populations of myopic best repliers, better repliers and imitators. In each period, one individual from each of n populations, one for each player role, is drawn to play and chooses a pure strategy according to her personal learning rule after observing a sample from a finite history. With a small probability individuals also make a mistake and play a pure strategy at random. I prove that, for a sufficiently low ratio between the sample and history size, only pure-strategy profiles in certain minimal closed sets under better replies will be played with positive probability in the limit, as the probability of mistakes tends to zero. If, in addition, the strategy profiles in one such set have strictly higher payoffs than all other strategy profiles and the sample size is sufficiently large, then the strategies in this set will be played with probability one in the limit. Applied to 2x2 Coordination Games, the Pareto dominant equilibrium is selected for a sufficiently large sample size, but in all symmetric and many asymmetric games, the risk dominant equilibrium is selected for a sufficiently small sample size.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 475.

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Length: 25 pages
Date of creation: 15 Nov 2001
Date of revision:
Handle: RePEc:hhs:hastef:0475

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Related research

Keywords: Bounded rationality; Evolutionary game theory; Imitation; Better replies; Markov chain; Stochastic stability; Pareto dominance; Risk dominance;

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  1. Saez-Marti, Maria & Weibull, Jörgen W., 1998. "Clever agents in Young's evolutionary bargaining model," Working Paper Series in Economics and Finance 281, Stockholm School of Economics.
  2. Burkhard Hehenkamp & Oddvar Kaarbøe, 2004. "Imitators and Optimizers in a Changing Environment," Discussion Papers in Economics 02_01, University of Dortmund, Department of Economics.
  3. Angelo Antoci & Antonio Gay & Massimiliano Landi & Pier Luigi Sacco, 2007. "Global Analysis of an Expectations Augmented Evolutionary Dynamics," Working Papers 25-2007, Singapore Management University, School of Economics.
  4. Kaarboe, O.M. & Tieman, A.F., 1999. "Equilibrium Selection under Different Learning Modes in Supermodular Games," Norway; Department of Economics, University of Bergen 1299, Department of Economics, University of Bergen.
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  7. Josephson, Jens & Matros, Alexander, 2000. "Stochastic Imitation in Finite Games," Working Paper Series in Economics and Finance 363, Stockholm School of Economics, revised 26 Nov 2002.
  8. Dawid, Herbert, 2007. "Evolutionary game dynamics and the analysis of agent-based imitation models: The long run, the medium run and the importance of global analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 2108-2133, June.
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  13. Josephson, Jens, 2008. "A numerical analysis of the evolutionary stability of learning rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1569-1599, May.
  14. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
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  17. J. Thijssen, 2005. "Nearly-complete Decomposability and Stochastic Stability with an Application to Cournot Oligopoly," Trinity Economics Papers tep6, Trinity College Dublin, Department of Economics.
  18. Kaniovski, Yuri M. & Kryazhimskii, Arkadii V. & Young, H. Peyton, 2000. "Adaptive Dynamics in Games Played by Heterogeneous Populations," Games and Economic Behavior, Elsevier, vol. 31(1), pages 50-96, April.
  19. Jens Josephson, 2008. "Stochastic better-reply dynamics in finite games," Economic Theory, Springer, vol. 35(2), pages 381-389, May.
  20. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
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Cited by:
  1. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2011. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 1112, University of California, Davis, Department of Economics.
  2. Dziubiński, Marcin & Roy, Jaideep, 2012. "Popularity of reinforcement-based and belief-based learning models: An evolutionary approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 433-454.

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