Existence of perfect equilibria: a direct proof

Iryna Topolyan ()

Economic Theory, 2013, vol. 53, issue 3, 697-705

Abstract: 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. Copyright Springer-Verlag 2013

Keywords: Perfect equilibrium; Best response correspondence; Unit simplex; Straight-line homotopy; Fixed point; C70; C72 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00199-012-0701-7

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