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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
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)
You can help add them by filling out this form.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Krannert PHD).
If references are entirely missing, you can add them using this form.