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Fast Convergence in Evolutionary Equilibrium Selection

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Listed author(s):
  • H Peyton Young
  • Gabriel E. Kreindler

Abstract

Stochastic learning models provide sharp predictions about equilibrium selection when the noise level of the learning process is taken to zero. The difficulty is that, when the noise is extremely small, it can take an extremely long time for a large population to reach the stochastically stable equilibrium. An important exception arises when players interact locally in small close-knit groups; in this case convergence can be rapid for small noise and an arbitrarily large population. We show that a similar result holds when the population is fully mixed and there is no local interaction. Selection is sharp and convergence is fast when the noise level is 'fairly' small but not extremely small.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 569.

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Date of creation: 01 Sep 2011
Handle: RePEc:oxf:wpaper:569
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Keywords: Stochastic stability; Logit learning; Markov chain; Convergence time;

Other versions of this item:

Find related papers by 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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  1. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
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  9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  10. Blume, Lawrence E., 2003. "How noise matters," Games and Economic Behavior, Elsevier, vol. 44(2), pages 251-271, August.
  11. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
  12. Dunia López-Pintado, 2006. "Contagion and coordination in random networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 371-381, October.
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  14. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
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Cited by:

  1. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
  2. Newton, Jonathan & Angus, Simon D., 2015. "Coalitions, tipping points and the speed of evolution," Journal of Economic Theory, Elsevier, vol. 157(C), pages 172-187.
  3. Ellison, Glenn & Fudenberg, Drew & Imhof, Lorens A., 2016. "Fast convergence in evolutionary models: A Lyapunov approach," Journal of Economic Theory, Elsevier, vol. 161(C), pages 1-36.
  4. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.
  5. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
  6. repec:eee:jeborg:v:138:y:2017:i:c:p:63-68 is not listed on IDEAS
  7. Levine, David Knudsen & Modica, Salvatore, 2016. "Dynamics in stochastic evolutionary models," Theoretical Economics, Econometric Society, vol. 11(1), January.
  8. Marden, Jason R. & Shamma, Jeff S., 2015. "Game Theory and Distributed Control****Supported AFOSR/MURI projects #FA9550-09-1-0538 and #FA9530-12-1-0359 and ONR projects #N00014-09-1-0751 and #N0014-12-1-0643," Handbook of Game Theory with Economic Applications, Elsevier.
  9. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
  10. H Peyton Young & Gabriel E. Kreindler, 2012. "Rapid Innovation Diffusion in Social Networks," Economics Series Working Papers 626, University of Oxford, Department of Economics.
  11. Lim, Wooyoung & Neary, Philip R., 2016. "An experimental investigation of stochastic adjustment dynamics," Games and Economic Behavior, Elsevier, vol. 100(C), pages 208-219.
  12. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.

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