Journal article

On Equilibrium Existence In Payoff Secure Games

Year:

2010

Published in:

Economic Theory
Discontinuous game
Payoff security
Transfer lower semicontinuity
Approximate Nash equilibrium
Reny’s theorem

We propose a single framework for studying the existence of approximate and exact pure strategy equilibria in payoff secure games. Central to the framework is the notion of a multivalued mapping with the local intersection property. By means of the Fan-Browder collective fixed point theorem, we first show an approximate equilibrium existence theorem that covers a number of known games. Then a short proof of Reny’s (Econometrica 67:1029–1056, 1999) equilibrium existence theorem is provided for payoff secure games with metrizable strategy spaces. We also give a simple proof of Reny’s theorem in its general form for metric games in an appendix for the sake of completeness.

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Publisher: International Scientific and Technical Conference “SOURCE OF TECHNOLOGIES OF BIOMEDICAL ENGINEERING”

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