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Stochastic evolution with slow learning


  • Alan Beggs

    () (Wadham College, Oxford OX1 3PN, UK)


This paper studies the extent to which diffusion approximations provide a reliable guide to equilibrium selection results in finite games. It is shown that they do for a class of finite games with weak learning provided that limits are taken in a certain order. The paper also shows that making mutation rates small does not in general select a unique equilibrium but making selection strong does.

Suggested Citation

  • Alan Beggs, 2002. "Stochastic evolution with slow learning," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(2), pages 379-405.
  • Handle: RePEc:spr:joecth:v:19:y:2002:i:2:p:379-405 Note: Received: January 19, 2000; revised version: September 25, 2000

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    References listed on IDEAS

    1. Itoh Hideshi, 1993. "Coalitions, Incentives, and Risk Sharing," Journal of Economic Theory, Elsevier, vol. 60(2), pages 410-427, August.
    2. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
    3. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    4. Dilip Mookherjee, 1984. "Optimal Incentive Schemes with Many Agents," Review of Economic Studies, Oxford University Press, vol. 51(3), pages 433-446.
    5. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    6. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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    Cited by:

    1. Dai, Darong, 2010. "一般化Moran过程中的合作演化
      [The Evolution of Cooperation in a Generalized Moran Process]
      ," MPRA Paper 40261, University Library of Munich, Germany.
    2. Dai, Darong, 2010. "The Evolution of Cooperation in a Generalized Moran Process," MPRA Paper 40511, University Library of Munich, Germany.
    3. Beggs, A.W., 2007. "Large deviations and equilibrium selection in large populations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 383-410, January.
    4. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Gotts, Nicholas M. & Polhill, J. Gary, 2007. "Transient and asymptotic dynamics of reinforcement learning in games," Games and Economic Behavior, Elsevier, vol. 61(2), pages 259-276, November.
    5. Sandholm,W.H., 1999. "Markov evolution with inexact information," Working papers 15, Wisconsin Madison - Social Systems.
    6. Dai, Darong, 2012. "Learning Nash Equilibria," MPRA Paper 40040, University Library of Munich, Germany.
    7. Sandholm, William H., 2003. "Evolution and equilibrium under inexact information," Games and Economic Behavior, Elsevier, vol. 44(2), pages 343-378, August.

    More about this item


    Equilibrium selection; Diffusion approximation; Evolutionary game theory; Risk dominance.;

    JEL classification:

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


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