# On pure-strategy equilibria in games with correlated information

*M. Ali Khan* and
*Yongchao Zhang* ()

*Games and Economic Behavior*, 2018, vol. 111, issue C, 289-304

**Abstract:**
This paper rehabilitates a program initiated in Aumann (1974) by contributing a result to the theory of finite-player Bayesian games in environments that explicitly include correlated information. An equivalence theorem offers conditions under which the set of mixed-strategy equilibrium payoffs in a classical finite-action game of complete information coincides with the set of objective pure-strategy Nash equilibrium (PSNE) expected payoffs in an affiliated Bayesian game with type-independent payoffs. This result is motivated for a non-specialist reader by several examples. An Appendix devoted to an intuitive discussion of the so-called ‘Lebesgue extension’ is added to make the paper self-contained.

**Keywords:** Bayesian games; Pure-strategy equilibrium; Correlated information; Atomless independent supplement; Radner–Rosenthal (RR) example (search for similar items in EconPapers)

**JEL-codes:** C62 D50 D82 G13 (search for similar items in EconPapers)

**Date:** 2018

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:gamebe:v:111:y:2018:i:c:p:289-304

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