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Equilibria with discontinuous preferences: new fixed point theorems. (English) Zbl 1510.91007

Summary: We prove new equilibrium existence results for games and economies with discontinuous and non-ordered preferences. To do so, we introduce the notion of “continuous inclusion property”, and prove new fixed point theorems which extend and generalize the results of K. Fan [Proc. Natl. Acad. Sci. USA 38, 121–126 (1952; Zbl 0047.35103)], I. L. Glicksberg [Proc. Am. Math. Soc. 3, 170–174 (1952; Zbl 0046.12103)], F. E. Browder [Math. Ann. 177, 283–301 (1968; Zbl 0176.45204)], and D. Gale and A. Mas-Colell [J. Math. Econ. 2, 9–15 (1975; Zbl 0324.90010)]. Our results also extend the previous work of N. C. Yannelis [J. Math. Anal. Appl. 108, 595–599 (1985; Zbl 0581.90010)] and X. Wu and S. Shen [J. Math. Anal. Appl. 197, No. 1, 61–74 (1996; Zbl 0852.54019)].

MSC:

91A10 Noncooperative games
91B50 General equilibrium theory
91A44 Games involving topology, set theory, or logic
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