Existence of Perfect Equilibria: A Direct Proof

I. Topolyan

Purdue University Economics Working Papers from Purdue University, Department of Economics

Abstract: We formulate and prove a modification of Eilenberg-Montgomery fixed-point theorem, which is a generalization of Kakutani s theorem. It enables us to provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. We construct a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by the modified version of Eilenberg-Montgomery theorem.

Keywords: Perfect equilibrium; best response correspondence; unit simplex; absolute neighborhood retract; deformation retract; fixed point (search for similar items in EconPapers)
JEL-codes: C7 (search for similar items in EconPapers)
Pages: 9 pages
Date: 2009-10
New Economics Papers: this item is included in nep-gth and nep-hpe
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Persistent link: https://EconPapers.repec.org/RePEc:pur:prukra:1226

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