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Stochastic adaptation in finite games played by heterogeneous populations

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  • Josephson, Jens

Abstract

We analyze stochastic adaptation in finite n-player games played by heterogeneous populations containing best repliers, better repliers, and imitators. Individuals select strategies by applying a personal learning rule to a sample from a finite history of past play. We give sufficient conditions for convergence to minimal closed sets under better replies and selection of a Pareto dominant such set. Finally, we demonstrate that the stochastically stable states are sensitive to the sample size by showing convergence to the risk-dominant equilibrium for sufficiently small sample size and to the Pareto-dominant equilibrium for sufficiently large sample size in 2x2 coordination games.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 33 (2009)
Issue (Month): 8 (August)
Pages: 1543-1554

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Handle: RePEc:eee:dyncon:v:33:y:2009:i:8:p:1543-1554

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Web page: http://www.elsevier.com/locate/jedc

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Keywords: Heterogeneous agents Markov chain Stochastic stability Pareto dominance Risk dominance;

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References

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  1. Matros, Alexander, 2000. "Clever agents in adaptive learning," Working Paper Series in Economics and Finance 403, Stockholm School of Economics.
  2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
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  9. 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.
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  13. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  14. 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.
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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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