Existence of Nash equilibria for generalized games without upper semicontinuity

Existence of Nash equilibria for generalized games without upper semicontinuity

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Article ID: iaor19982899
Country: Germany
Volume: 26
Issue: 2
Start Page Number: 267
End Page Number: 273
Publication Date: Jan 1997
Journal: International Journal of Game Theory
Authors:
Keywords: Nash theory and methods
Abstract:

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.

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