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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.

MSC:
91A10 Noncooperative games
91A05 2-person games
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