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Stochastic imitation in finite games

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  • Josephson, Jens
  • Matros, Alexander

Abstract

In this paper we model an evolutionary process with perpetual random shocks where individual behavior is determined by imitation. Every period an agent is randomly chosen from each of n finite populations to play a game. Each agent observes a sample of population-specific past strategy and payoff realizations. She thereafter imitates by choosing the strategy with highest average payoff in the sample. Occasionally the agents also experiment or make mistakes and choose a strategy at random. For finite n-player games we prove that in the limit, as the probability of experimentation tends to zero, only strategy-tuples in minimal sets closed under the better-reply graph will be played with positive probability. If the strategy-tuples in one such minimal set have strictly higher payoffs than all outside strategy-tuples, then the strategy-tuples in this set will be played with probability one in the limit, provided the minimal set is a product set. We also show that in 2x2 games the convergence in our model is faster than in other known models.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 49 (2004)
Issue (Month): 2 (November)
Pages: 244-259

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Handle: RePEc:eee:gamebe:v:49:y:2004:i:2:p:244-259

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Web page: http://www.elsevier.com/locate/inca/622836

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  2. Apestgeguia, Jose & Huck, Steffen & Oechssler, Jörg, 2005. "Imitation - Theory and Experimental Evidence," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 54, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
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  12. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
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  14. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
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Citations

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Cited by:
  1. Alexander Matros, 2006. "Location, Information and Coordination," Working Papers 307, University of Pittsburgh, Department of Economics, revised May 2007.
  2. Bergin, James & Bernhardt, Dan, 2009. "Cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 67(2), pages 376-388, November.
  3. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
  4. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2007. "Ordinal Games," CER-ETH Economics working paper series 07/74, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    • Jacques Durieu & Hans Haller & Nicolas Quérou & Philippe Solal, 2007. "Ordinal Games," Post-Print ujm-00194794, HAL.
  5. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
  6. Tsakas, Nikolas, 2012. "Naive learning in social networks: Imitating the most successful neighbor," MPRA Paper 37796, University Library of Munich, Germany.
  7. Saran Rene & Serrano Roberto, 2010. "Regret Matching with Finite Memory," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  8. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Working Papers 2010-10, Brown University, Department of Economics.
  9. Josephson, Jens, 2001. "Stochastic Adaptation in Finite Games Played by Heterogeneous Populations," Working Paper Series in Economics and Finance 475, Stockholm School of Economics.
  10. Matthey, Astrid, 2010. "Imitation with intention and memory: An experiment," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 39(5), pages 585-594, October.
  11. Pascal Billand & Christophe Bravard, 2006. "Les modèles de comportements adaptatifs appliqués à l'oligopole de Cournot," Post-Print ujm-00121658, HAL.

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