Existence of perfect equilibria: a direct proof by Iryna Topolyan

By:

Topolyan, Iryna [author]

Material type: Text

TextSeries: Economic theory ; Volume 53, number 3Heildelberg : Springer, 2013Content type:

text

Media type:

unmediated

Carrier type:

volume

ISSN:

0938-2259

Subject(s):

Perfect equilibri

LOC classification:

HB119 ECO

Online resources:

Click here to access online

Summary: We provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. It is done by constructing a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by a generalization of Kakutani theorem, which is proved in this paper. This work offers a new approach to perfect equilibria, which would hopefully facilitate further study on this topic. We also hope our direct proof would be the first step toward building an algorithm to find the set of all perfect equilibria of a strategic game.

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Holdings
Item type	Current library	Call number	Vol info	Copy number	Status	Notes	Date due	Barcode
Journal Article	Main Library - Special Collections	HB119 ECO (Browse shelf(Opens below))	vol. 53, no. 3 (pages 697-705)	SP21043	Not for loan	For In house Use

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We provide a direct proof of the existence of perfect equilibria in finite normal form games and extensive games with perfect recall. It is done by constructing a correspondence whose fixed points are precisely the perfect equilibria of a given finite game. Existence of a fixed point is secured by a generalization of Kakutani theorem, which is proved in this paper. This work offers a new approach to perfect equilibria, which would hopefully facilitate further study on this topic. We also hope our direct proof would be the first step toward building an algorithm to find the set of all perfect equilibria of a strategic game.

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