# Nash and Bayes–Nash equilibria in strategic-form games with intransitivities

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## Abstract

We study games with intransitive preferences that admit skew-symmetric representations. We introduce the notion of surrogate better-reply security for discontinuous skew-symmetric games and elucidate the relationship between surrogate better-reply security and other security concepts in the literature. We then prove existence of behavioral strategy equilibrium for discontinuous skew-symmetric games of incomplete information (and, in particular, existence of mixed-strategy equilibrium for discontinuous skew-symmetric games of complete information), generalizing extant results.

## Keywords

Skew-symmetric game Bayesian game Existence of Nash equilibrium Discontinuous game Behavioral strategy## JEL classification

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