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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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References

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  1. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  2. Jose Alpesteguia & Steffen Huck & Jörg Oechssler, 2003. "Imitation - Theory and Experimental Evidence," CESifo Working Paper Series 1049, CESifo Group Munich.
  3. G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
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  5. Osborne, M-J & Rubinstein, A, 1997. "Games with Procedurally Rational Players," Papers 4-97, Tel Aviv.
  6. Arthur J Robson & Fernando Vega-Redondo, 1999. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Levine's Working Paper Archive 2112, David K. Levine.
  7. 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.
  8. Sobel, Joel, 1993. "Evolutionary stability and efficiency," Economics Letters, Elsevier, vol. 42(2-3), pages 301-312.
  9. Nick Feltovich & John Duffy, 1999. "Does observation of others affect learning in strategic environments? An experimental study," International Journal of Game Theory, Springer, vol. 28(1), pages 131-152.
  10. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 1999. "Learning in Cournot Oligopoly--An Experiment," Economic Journal, Royal Economic Society, vol. 109(454), pages C80-95, March.
  11. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  12. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  13. Griffiths, Mark D. & Smith, Brian F. & Turnbull, D. Alasdair S. & White, Robert W., 1998. "Information flows and open outcry: evidence of imitation trading," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 8(2), pages 101-116, June.
  14. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 1998. "Does information about competitors' actions increase or decrease competition in experimental oligopoly markets?," Industrial Organization 9803004, EconWPA.
  15. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  16. Russ Wermers, 1999. "Mutual Fund Herding and the Impact on Stock Prices," Journal of Finance, American Finance Association, vol. 54(2), pages 581-622, 04.
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Citations

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Cited by:
  1. 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.
  2. James Bergin & Dan Bernhardt, 2006. "Cooperation through Imitation," Working Papers 1042, Queen's University, Department of Economics.
  3. Rene Saran & Roberto Serrano, 2010. "Regret Matching with Finite Memory," Levine's Working Paper Archive 661465000000000078, David K. Levine.
  4. 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.
  5. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
  6. Alexander Matros, 2006. "Location, Information and Coordination," Working Papers 307, University of Pittsburgh, Department of Economics, revised May 2007.
  7. Astrid Matthey, 2006. "Imitation with Intention and Memory: an Experiment," SFB 649 Discussion Papers SFB649DP2006-088, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Tsakas, Nikolas, 2012. "Naive learning in social networks: Imitating the most successful neighbor," MPRA Paper 37796, University Library of Munich, Germany.
  9. Pascal Billand & Christophe Bravard, 2006. "Les modèles de comportements adaptatifs appliqués à l'oligopole de Cournot," Post-Print ujm-00121658, HAL.
  10. 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.
  11. 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).

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