Existence of Perfect Equilibria: A Direct Proof
AbstractWe 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.
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Bibliographic InfoPaper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1226.
Length: 9 pages
Date of creation: Oct 2009
Date of revision:
Perfect equilibrium; best response correspondence; unit simplex; absolute neighborhood retract; deformation retract; fixed point;
Find related papers by JEL classification:
- C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-08-28 (All new papers)
- NEP-GTH-2010-08-28 (Game Theory)
- NEP-HPE-2010-08-28 (History & Philosophy of Economics)
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