International Journal of Game Theory

, Volume 46, Issue 1, pp 167–183

Existence of pure-strategy equilibria in Bayesian games: a sharpened necessity result

Original Paper

DOI: 10.1007/s00182-016-0528-8

Cite this article as:
Khan, M.A. & Zhang, Y. Int J Game Theory (2017) 46: 167. doi:10.1007/s00182-016-0528-8


In earlier work, the authors showed that a pure-strategy Bayesian-Nash equilibria in games with uncountable action sets and atomless private information spaces may not exist if the information space of each player is not saturated. This paper sharpens this result by exhibiting a failure of the existence claim for a game in which the information space of only one player is not saturated. The methodology that enables this extension of the necessity theory is novel relative to earlier work, and its conceptual underpinnings may have independent interest.


Bayesian games Pure-strategy Nash equilibrium (PSNE) Khan-Rath-Sun game (KRS game) Saturated probability spaces 

JEL Classification

C62 D50 D82 G13 

Funding information

Funder NameGrant NumberFunding Note
National Natural Science Foundation of China
  • 11201283

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of EconomicsThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.School of EconomicsShanghai University of Finance and EconomicsShanghaiChina
  3. 3.Key Laboratory of Mathematical Economics (SUFE)Ministry of EducationShanghaiChina

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