On the existence of pure-strategy equilibria in games with private information: A complete characterization

M. Khan and Yongchao Zhang ()

Journal of Mathematical Economics, 2014, vol. 50, issue C, 197-202

Abstract: This paper reports a definitive resolution to the question of the existence of a pure-strategy Bayesian–Nash equilibrium in games with a finite number of players, each with a compact metric action set and private information. The resolution hinges on saturated spaces. If the individual spaces of information are saturated, there exists a pure-strategy equilibrium in such a game; and if there exists a pure-strategy equilibrium for the class of games under consideration and with uncountable action sets, the spaces of private information must be saturated. As such, the paper offers a complete characterization of a longstanding question, and offers another game-theoretic characterization of the saturation property, one that complements a recent result of Keisler–Sun (2009) on large non-anonymous games with complete information.

Keywords: Pure-strategy Bayesian–Nash equilibrium; Private information games; Saturated probability space (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:50:y:2014:i:c:p:197-202

DOI: 10.1016/j.jmateco.2013.12.005

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