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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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Citations

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Cited by:
  1. Josephson, Jens, 2009. "Stochastic adaptation in finite games played by heterogeneous populations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1543-1554, August.
  2. Tsakas, Nikolas, 2012. "Naive learning in social networks: Imitating the most successful neighbor," MPRA Paper 37796, University Library of Munich, Germany.
  3. Rene Saran & Roberto Serrano, 2010. "Regret matching with finite memory," Working Papers 2010-10, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  4. 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).
  5. Astrid Matthey, 2006. "Imitation with Intention and Memory: an Experiment," SFB 649 Discussion Papers SFB649DP2006-088, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Jacques Durieu & Hans Haller & Nicolas Quérou & Philippe Solal, 2007. "Ordinal Games," Post-Print ujm-00194794, HAL.
  7. Alexander Matros, 2006. "Location, Information and Coordination," Working Papers 307, University of Pittsburgh, Department of Economics, revised May 2007.
  8. 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.
  9. Bergin, James & Bernhardt, Dan, 2009. "Cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 67(2), pages 376-388, November.
  10. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
  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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