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A Short Proof of Reny's Existence Theorem for Payoff Secure Games

Pavlo Prokopovych

No 12, Discussion Papers from Kyiv School of Economics

Abstract: A short proof of Reny (1999)'s equilibrium existence theorem for payoff secure games is provided. At the heart of the proof lies the concept of a multivalued mapping with the local intersection property. By means of the Fan-Browder collective fixed-point theorem, we show an approximate equilibrium existence theorem which covers a number of known games. Reny's theorem follows from it straightforwardly.

Keywords: Discontinuous game; payoff security; transfer lower semicontinuity; approximate Nash equilibrium; Reny's theorem (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Date: 2008-12
New Economics Papers: this item is included in nep-gth and nep-hpe
Note: Published in Economic Theory DOI 10.1007/s00199-010-0526-1S
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