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A Multinomial Probit Model of Stochastic Evolution

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Author Info
David P. Myatt
Chris Wallace

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Abstract

A strategy revision process in symmetric normal form games is proposed. Following Kandori, Mailath, and Rob (1993), members of a population periodically revise their strategy choice, and choose a myopic best response to currently observed play. Their payoffs are perturbed by normally distributed Harsanyian (1973) trembles, so that strategies are chosen according to multinomial probit probabilities. As the variance of payoffs is allowed to vanish, the graph theoretic methods of the earlier literature continue to apply. The distributional assumption enables a convenient closed form characterisation for the weights of the rooted trees. An illustration of the approach is offered, via a consideration of the role of dominated strategies in equilibrium selection.

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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 090.

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Date of creation: 2002
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Handle: RePEc:oxf:wpaper:090

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Keywords: multinational probit stochastic evolution idiosyncrasy dominated strategies

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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

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Toshimasa Maruta, 1995. "On the Relationship Between Risk-Dominance and Stochastic Stability," Discussion Papers 1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  2. David P. Myatt & Chris Wallace, 2002. "Adaptive Play by Idiosyncratic Agents," Economics Series Working Papers 089, University of Oxford, Department of Economics. [Downloadable!]
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  3. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-56, July. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
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  6. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Blackwell Publishing, vol. 67(1), pages 17-45, January.
  7. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  8. Lawrence E. Blume, 1994. "How Noise Matters," Game Theory and Information 9407002, EconWPA, revised 27 Jul 1994. [Downloadable!]
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  9. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-57, January. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. David P. Myatt & Chris Wallace, 2006. "When An Evolutionary Analysis of the Volunteer`s Dilemma," Economics Series Working Papers 270, University of Oxford, Department of Economics. [Downloadable!]
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