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Stochastic Imitation in Finite Games

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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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 363.

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Length: 33 pages
Date of creation: 09 Mar 2000
Date of revision: 26 Nov 2002
Handle: RePEc:hhs:hastef:0363

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Keywords: Evolutionary game theory; bounded rationality; imitation; Markov chain; stochastic stability; better replies; Pareto dominance;

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  1. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  2. Jose Apesteguia & Steffen Huck & Jorg Oechssler, 2003. "Imitation - Theory and Experimental Evidence," Experimental 0309001, EconWPA.
  3. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  4. Sobel, Joel, 1993. "Evolutionary stability and efficiency," Economics Letters, Elsevier, vol. 42(2-3), pages 301-312.
  5. John Duffy & Nick Feltovich, 1997. "Does Observation of Others Affect Learning in Strategic Environments? An Experimental Study," Levine's Working Paper Archive 592, David K. Levine.
  6. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  7. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 2000. "Does information about competitors' actions increase or decrease competition in experimental oligopoly markets?," International Journal of Industrial Organization, Elsevier, vol. 18(1), pages 39-57, January.
  8. G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
  9. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  10. 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.
  11. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-47, September.
  12. 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.
  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. 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.
  15. John R. Graham, 1999. "Herding among Investment Newsletters: Theory and Evidence," Journal of Finance, American Finance Association, vol. 54(1), pages 237-268, 02.
  16. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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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," Working Papers 2010-10, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  4. Tsakas, Nikolas, 2012. "Naive learning in social networks: Imitating the most successful neighbor," MPRA Paper 37796, University Library of Munich, Germany.
  5. 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).
  6. 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.
  7. Jacques Durieu & Hans Haller & Nicolas Quérou & Philippe Solal, 2007. "Ordinal Games," Post-Print ujm-00194794, HAL.
  8. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
  9. Alexander Matros, 2006. "Location, Information and Coordination," Working Papers 307, University of Pittsburgh, Department of Economics, revised May 2007.
  10. Josephson, Jens, 2001. "Stochastic Adaptation in Finite Games Played by Heterogeneous Populations," Working Paper Series in Economics and Finance 475, Stockholm School of Economics.
  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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