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Existence of Nash equilibria for generalized games without upper semicontinuity. (English) Zbl 0881.90134

Summary: The present note extends Debreu’s equilibrium existence theorem for a generalized game in the context of finite-dimensional strategy spaces, by weakening the upper semicontinuity and closed-valuedness assumption on the feasible strategy multifunctions. This is made by establishing an inequality of Ky Fan’s type, whose proof is based on a selection theorem by E. Michael. An extension to generalized games with unbounded strategy spaces is also presented.

MSC:

91A10 Noncooperative games
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