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Stochastic Imitation in Finite Games

Author

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  • Josephson, Jens

    (Dept. of Economics, Stockholm School of Economics)

  • Matros, Alexander

    (Stockholm Institute of Transition Economics and East European Economies)

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.

Suggested Citation

  • Josephson, Jens & Matros, Alexander, 2000. "Stochastic Imitation in Finite Games," SSE/EFI Working Paper Series in Economics and Finance 363, Stockholm School of Economics, revised 27 Nov 2002.
  • Handle: RePEc:hhs:hastef:0363
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    Cited by:

    1. Pascal Billand & Christophe Bravard, 2006. "Les modèles de comportements adaptatifs appliqués à l'oligopole de Cournot," Revue d'économie industrielle, De Boeck Université, vol. 0(2), pages 9-9.
    2. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    3. 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.
    4. Tsakas, Nikolas, 2012. "Naive learning in social networks: Imitating the most successful neighbor," MPRA Paper 37796, University Library of Munich, Germany.
    5. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    6. Alexander Matros, 2006. "Location, Information and Coordination," Working Paper 307, Department of Economics, University of Pittsburgh, revised May 2007.
    7. 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.
    8. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    9. Bergin, James & Bernhardt, Dan, 2009. "Cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 67(2), pages 376-388, November.
    10. Abhimanyu Khan, 2021. "Evolution of conventions in games between behavioural rules," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 209-224, October.
    11. 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.
    12. Jacques Durieu & Philippe Solal, 2012. "Models of Adaptive Learning in Game Theory," Chapters, in: Richard Arena & Agnès Festré & Nathalie Lazaric (ed.), Handbook of Knowledge and Economics, chapter 11, Edward Elgar Publishing.
    13. Khan, Abhimanyu, 2018. "Games between responsive behavioural rules," MPRA Paper 90429, University Library of Munich, Germany.
    14. Napel, Stefan, 2003. "Aspiration adaptation in the ultimatum minigame," Games and Economic Behavior, Elsevier, vol. 43(1), pages 86-106, April.
    15. 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.

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    More about this item

    Keywords

    Evolutionary game theory; bounded rationality; imitation; Markov chain; stochastic stability; better replies; Pareto dominance;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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