zbMATH — the first resource for mathematics

A multinomial probit model of stochastic evolution. (English) Zbl 1158.91307
Summary: A strategy revision process in symmetric normal form games is proposed. Following M. Kandori, G. J. Mailath and R. Rob [Econometrica 61, No. 1, 29–56 (1993; Zbl 0776.90095)], 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 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.

91A10 Noncooperative games
91A05 2-person games
Full Text: DOI
[1] Bergin, J.; Lipman, B., Evolution with state-dependent mutations, Econometrica, 64, 943-956, (1996) · Zbl 0862.90142
[2] L.E. Blume, How noise matters, Working Paper, Santa Fe Institute, 1999.
[3] Ellison, G., Basins of attraction, long run stochastic stability and the speed of step-by-step evolution, Rev. econom. stud., 67, 17-46, (2000) · Zbl 0956.91027
[4] Freidlin, M.I.; Wentzell, A.D., Random perturbations of dynamical systems, (1984), Springer Berlin · Zbl 0522.60055
[5] Grimmett, G.R.; Stirzaker, D.R., Probability and random processes, (2001), Oxford University Press Oxford · Zbl 0759.60002
[6] Harsanyi, J.C., Games with randomly disturbed payoffsa new rationale for mixed-strategy equilibrium points, Int. J. game theory, 2, 1-23, (1973) · Zbl 0255.90084
[7] Harsanyi, J.C.; Selten, R., A general theory of equilibrium selection in games, (1988), MIT Press Cambridge, MA · Zbl 0693.90098
[8] Kandori, M.; Mailath, G.J.; Rob, R., Learning, mutation and long-run equilibria in games, Econometrica, 61, 29-56, (1993) · Zbl 0776.90095
[9] Maruta, T., On the relationship between risk-dominance and stochastic stability, Games econom. behav., 19, 221-234, (1997)
[10] Morris, S.; Rob, R.; Shin, H.S., Dominance and belief potential, Econometrica, 63, 145-157, (1995) · Zbl 0827.90138
[11] D.P. Myatt, C. Wallace, Adaptive play by idiosyncratic agents, Discussion Paper 89, Department of Economics, Oxford University, 2002. · Zbl 1117.91011
[12] P.A. Ruud, Approximation and simulation of the multinomial probit model: An analysis of covariance matrix estimation, Working Paper, University of California, Berkeley, 1996.
[13] Vega-Redondo, F., The evolution of Walrasian behavior, Econometrica, 65, 375-384, (1997) · Zbl 0874.90049
[14] Young, H.P., The evolution of conventions, Econometrica, 61, 57-84, (1993) · Zbl 0773.90101
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.