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On the existence of equilibria in games with arbitrary strategy spaces and preferences

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  • Tian, Guoqiang

Abstract

This paper provides necessary and sufficient conditions for the existence of pure strategy Nash equilibria by replacing the assumptions concerning continuity and quasiconcavity with a unique condition, passing strategy space from topological vector spaces to arbitrary topological spaces. Preferences may also be nontotal/nontransitive, discontinuous, nonconvex, or nonmonotonic. We define a single condition, recursive diagonal transfer continuity (RDTC) for aggregator payoff function and recursive weak transfer quasi-continuity (RWTQC) for individuals’ preferences, respectively, which establishes the existence of pure strategy Nash equilibria in games with arbitrary (topological) strategy spaces and preferences without imposing any kind of quasiconcavity-related conditions.

Suggested Citation

  • Tian, Guoqiang, 2015. "On the existence of equilibria in games with arbitrary strategy spaces and preferences," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 9-16.
    • Handle: RePEc:eee:mateco:v:60:y:2015:i:c:p:9-16
    DOI: 10.1016/j.jmateco.2015.06.001
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