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Stochastic Adaptation in Finite Games Played by Heterogeneous Populations

  • Josephson, Jens


    (Dept. of Economics, Stockholm School of Economics)

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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Paper provided by Stockholm School of Economics in its series SSE/EFI 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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  2. Matros, Alexander, 2000. "Clever agents in adaptive learning," SSE/EFI Working Paper Series in Economics and Finance 403, Stockholm School of Economics.
  3. Jens Josephson, 2008. "Stochastic better-reply dynamics in finite games," Economic Theory, Springer, vol. 35(2), pages 381-389, May.
  4. 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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  8. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
  9. Josephson, Jens & Matros, Alexander, 2004. "Stochastic imitation in finite games," Games and Economic Behavior, Elsevier, vol. 49(2), pages 244-259, November.
  10. 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.
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  17. Carlos Alós-Ferrer, 2001. "Cournot versus Walras in Dynamic Oligopolies with Memory," Vienna Economics Papers 0110, University of Vienna, Department of Economics.
  18. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  19. Weibull, Jörgen W. & Saez-Marti, Maria, 1998. "Clever Agents in Young's Evolutionary Bargaining Model," Working Paper Series 507, Research Institute of Industrial Economics.
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  23. 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.
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