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A Multinomial Probit Model of Stochastic Evolution

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  • David P. Myatt
  • Chris Wallace

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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Bibliographic Info

Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 90.

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Date of creation: 01 Mar 2002
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Handle: RePEc:oxf:wpaper:90

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Keywords: multinational probit; stochastic evolution; idiosyncrasy; dominated strategies;

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References

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  1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
  2. Ellison, Glenn, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 17-45, January.
  3. Myatt, David P. & Wallace, Chris C., 2004. "Adaptive play by idiosyncratic agents," Games and Economic Behavior, Elsevier, vol. 48(1), pages 124-138, July.
  4. Maruta, Toshimasa, 1997. "On the Relationship between Risk-Dominance and Stochastic Stability," Games and Economic Behavior, Elsevier, vol. 19(2), pages 221-234, May.
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Citations

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Cited by:
  1. Staudigl, Mathias, 2011. "Potential games in volatile environments," Games and Economic Behavior, Elsevier, vol. 72(1), pages 271-287, May.
  2. Carlos Alos-Ferrer & Nick Netzer, 2008. "The Logit-Response Dynamics," TWI Research Paper Series 28, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
  3. 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.
  4. Staudigl, Mathias, 2012. "Stochastic stability in asymmetric binary choice coordination games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 372-401.
  5. Kim, Chongmin & Wong, Kam-Chau, 2010. "Long-run equilibria with dominated strategies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 242-254, January.
  6. David P. Myatt & Chris Wallace, 2006. "An Evolutionary Analysis of the Volunteer`s Dilemma," Economics Series Working Papers 270, University of Oxford, Department of Economics.
  7. Carlos Alós–Ferrer & Nick Netzer, 2012. "Robust stochastic stability," ECON - Working Papers 063, Department of Economics - University of Zurich, revised Jan 2014.
  8. Dokumacı, Emin & Sandholm, William H., 2011. "Large deviations and multinomial probit choice," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2151-2158.
  9. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, Open Access Journal, vol. 1(4), pages 551-585, November.

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