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Pareto refinements of pure-strategy equilibria in games with public and private information

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  • Fu, Haifeng
  • Yu, Haomiao

Abstract

In a Bayesian framework with public and private information that allows countably many players and infinitely many actions, we provide two sufficient conditions that ensure the existence of Pareto-undominated and socially-maximal pure-strategy Bayes–Nash equilibria under the usual diffuseness and independence assumptions: every player has (i) a countable action set, or (ii) a relatively-diffuse strategy-relevant private information space conditioned on a public signal. Our results rely on the theory of distributions of correspondences with infinite-dimensional range and draw on notions of nowhere equivalence, relative saturation, and saturation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:79:y:2018:i:c:p:18-26
    DOI: 10.1016/j.jmateco.2018.09.005
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    1. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    2. M. Ali Khan & Yongchao Zhang, 2017. "Existence of pure-strategy equilibria in Bayesian games: a sharpened necessity result," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 167-183, March.
    3. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    4. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    5. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    6. Rath Kali P., 1994. "Some Refinements of Nash Equilibria of Large Games," Games and Economic Behavior, Elsevier, vol. 7(1), pages 92-103, July.
    7. Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
    8. Salonen, Hannu, 1996. "On the Existence of Undominated Nash Equilibria in Normal Form Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 208-219, June.
    9. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    10. Yi, Sang-Seung, 1999. "On the Coalition-Proofness of the Pareto Frontier of the Set of Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 26(2), pages 353-364, January.
    11. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1999. "On a private information game without pure strategy equilibria1," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 341-359, April.
    12. 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.
    13. Khan, M. Ali & Zhang, Yongchao, 2014. "On the existence of pure-strategy equilibria in games with private information: A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 197-202.
    14. Rath, Kali P., 1998. "Perfect and Proper Equilibria of Large Games," Games and Economic Behavior, Elsevier, vol. 22(2), pages 331-342, February.
    15. M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 91-104, April.
    16. Fu, Haifeng & Sun, Yeneng & Yannelis, Nicholas C. & Zhang, Zhixiang, 2007. "Pure strategy equilibria in games with private and public information," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 523-531, June.
    17. He, Wei & Sun, Xiang & Sun, Yeneng, 2017. "Modeling infinitely many agents," Theoretical Economics, Econometric Society, vol. 12(2), May.
    18. Yu, Haomiao & Zhang, Zhixiang, 2007. "Pure strategy equilibria in games with countable actions," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 192-200, February.
    19. Barelli, Paulo & Duggan, John, 2015. "Purification of Bayes Nash equilibrium with correlated types and interdependent payoffs," Games and Economic Behavior, Elsevier, vol. 94(C), pages 1-14.
    20. He, Wei & Sun, Xiang, 2014. "On the diffuseness of incomplete information game," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 131-137.
    21. Roy Radner & Robert W. Rosenthal, 1982. "Private Information and Pure-Strategy Equilibria," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 401-409, August.
    22. Fu, Haifeng & Yu, Haomiao, 2015. "Pareto-undominated and socially-maximal equilibria in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 7-15.
    23. He, Wei & Yannelis, Nicholas C., 2015. "Discontinuous games with asymmetric information: An extension of Reny's existence theorem," Games and Economic Behavior, Elsevier, vol. 91(C), pages 26-35.
    24. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, July.
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    1. Fu, Haifeng, 2021. "On the existence of Pareto undominated mixed-strategy Nash equilibrium in normal-form games with infinite actions," Economics Letters, Elsevier, vol. 201(C).

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