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Stochastic Imitation in Finite Games

  • Josephson, Jens

    ()

    (Dept. of Economics, Stockholm School of Economics)

  • Matros, Alexander

    (Stockholm Institute of Transition Economics and East European Economies)

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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File URL: http://swopec.hhs.se/hastef/papers/hastef0363.pdf
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Paper provided by Stockholm School of Economics in its series SSE/EFI 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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  1. Jose Apesteguia & Steffen Huck & Jorg Oechssler, 2004. "Imitation - Theory and Experimental Evidence," Levine's Bibliography 122247000000000132, UCLA Department of Economics.
  2. 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.
  3. 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.
  4. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  5. 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.
  6. Noldeke Georg & Samuelson Larry, 1993. "An Evolutionary Analysis of Backward and Forward Induction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 425-454, July.
  7. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  8. John R. Graham, 1999. "Herding among Investment Newsletters: Theory and Evidence," Journal of Finance, American Finance Association, vol. 54(1), pages 237-268, 02.
  9. 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.
  10. Sobel, Joel, 1993. "Evolutionary stability and efficiency," Economics Letters, Elsevier, vol. 42(2-3), pages 301-312.
  11. 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.
  12. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  13. 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.
  14. Osborne, M-J & Rubinstein, A, 1997. "Games with Procedurally Rational Players," Papers 4-97, Tel Aviv.
  15. 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.
  16. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  17. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
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