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The evolutionary stability of perfectly competitive behavior. (English) Zbl 1106.91002
This paper deals with the class of (generalized) symmetric aggregative games whose payoffs depend only on an individual strategy and an aggregate of all strategies. See also the articles by Dubey et al. [P. Dubey, A. Mas-Colell and M. Shubik, J. Econ. Theory 22, 339–362 (1980; Zbl 0443.90013)] and L. C. Corchón [Math. Soc. Sci. 28, 151–165 (1994; Zbl 0877.90091)] in this connection. Players behaving as if they were negligible would optimize taking the aggregate as given. The authors provide evolutionary and dynamic foundations for such behavior when the game satisfies supermodularity conditions. The results obtained in this paper are also useful to characterize evolutionarily stable strategies in a finite population.

MSC:
91A10 Noncooperative games
91A22 Evolutionary games
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