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On pure-strategy equilibria in games with correlated information

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  • Khan, M. Ali
  • Zhang, Yongchao

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.

Suggested Citation

  • Khan, M. Ali & Zhang, Yongchao, 2018. "On pure-strategy equilibria in games with correlated information," Games and Economic Behavior, Elsevier, vol. 111(C), pages 289-304.
    • Handle: RePEc:eee:gamebe:v:111:y:2018:i:c:p:289-304
    DOI: 10.1016/j.geb.2017.12.006
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    References listed on IDEAS

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    9. Konrad Podczeck, 2009. "On purification of measure-valued maps," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 399-418, February.
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    Cited by:

    1. Beißner, Patrick & Khan, M. Ali, 2019. "On Hurwicz–Nash equilibria of non-Bayesian games under incomplete information," Games and Economic Behavior, Elsevier, vol. 115(C), pages 470-490.
    2. Fu, Haifeng & Yu, Haomiao, 2018. "Pareto refinements of pure-strategy equilibria in games with public and private information," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 18-26.
    3. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    4. Khan, M. Ali & McLean, Richard P. & Uyanik, Metin, 2024. "On constrained generalized games with action sets in non-locally-convex and non-Hausdorff topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    5. He, Wei & Sun, Yeneng, 2019. "Pure-strategy equilibria in Bayesian games," Journal of Economic Theory, Elsevier, vol. 180(C), pages 11-49.

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    More about this item

    Keywords

    Bayesian games; Pure-strategy equilibrium; Correlated information; Atomless independent supplement; Radner–Rosenthal (RR) example;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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