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How noise matters

  • Blume, Lawrence E.

Recent advances in evolutionary game theory have employed stochastic processes of noise in decisionmaking to select in favor of certain equilibria in coordination games. Noisy decisionmaking is justified on bounded rationality grounds, and consequently the sources of noise are left unmodelled. This methodological approach can only be successful if the results do not depend too much on the nature of the noise process. This paper investigates invariance to noise of the equilibrium selection results, both for the random matching paradigm that has characterized much of the recent literature and for a larger class of two-strategy population games where payoffs may vary non-linearly with the distribution of strategies among the population. Several parametrizations of noise reduction are investigated. The results show that a symmetry property of the noise process and (in the case of non-linear payoffs) bounds on the asymmetry of the payoff functions suffice to preserve the selection results of the evolutionary literature.

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File URL: http://www.sciencedirect.com/science/article/B6WFW-48TKF28-1/2/cc9fb1fd7603fe2423bb4d1921f0e8fd
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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 44 (2003)
Issue (Month): 2 (August)
Pages: 251-271

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Handle: RePEc:eee:gamebe:v:44:y:2003:i:2:p:251-271
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, David K. Levine.
  2. D. Canning, 2010. "Average Behavior in Learning Models," Levine's Working Paper Archive 490, David K. Levine.
  3. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  4. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
  5. William Brock & Steven N. Durlauf, 2000. "Interactions-Based Models," NBER Technical Working Papers 0258, National Bureau of Economic Research, Inc.
  6. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  8. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  9. Samuelson Larry, 1994. "Stochastic Stability in Games with Alternative Best Replies," Journal of Economic Theory, Elsevier, vol. 64(1), pages 35-65, October.
  10. Brock,W.A. & Durlauf,S.N., 2000. "Discrete choice with social interactions," Working papers 7, Wisconsin Madison - Social Systems.
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