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Axiomatic characterizations of solutions for Bayesian games

Author

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  • van Heumen, R.W.J.
  • Peleg, B.
  • Tijs, S.H.

    (Tilburg University, School of Economics and Management)

  • Borm, P.E.M.

    (Tilburg University, School of Economics and Management)

Abstract

Bayesian equilibria are characterized by means of consistency and one-person rationality in combination with non-emptiness or converse consistency. Moreover, strong and coalition-proof Bayesian equilibria of extended Bayesian games are introduced and it is seen that these notions can be characterized by means of consistency, one-person rationality, a version of Pareto optimality and a modification of converse consistency. It is shown that, in case of the strong Bayesian equilibrium correspondence, converse consistency can be replaced by non-emptiness. As examples we treat Bayesian potential games and Bayesian congestion games.
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Suggested Citation

  • van Heumen, R.W.J. & Peleg, B. & Tijs, S.H. & Borm, P.E.M., 1994. "Axiomatic characterizations of solutions for Bayesian games," Other publications TiSEM b16fc7d9-aee7-4f36-95f2-3, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:b16fc7d9-aee7-4f36-95f2-3b62ed360b21
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    References listed on IDEAS

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    1. Norde, Henk & Potters, Jos & Reijnierse, Hans & Vermeulen, Dries, 1996. "Equilibrium Selection and Consistency," Games and Economic Behavior, Elsevier, vol. 12(2), pages 219-225, February.
    2. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    3. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
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    Cited by:

    1. van den Nouweland, A. & Peleg, B. & Tijs, S., 1996. "Axiomatic characterizations of the Walras correspondence for generalized economies," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 355-372.
    2. Giovanni Facchini & Freek van Megen & Peter Borm & Stef Tijs, 1997. "Congestion Models And Weighted Bayesian Potential Games," Theory and Decision, Springer, vol. 42(2), pages 193-206, March.
    3. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Concept of the Core of Games in Effectiveness Form," GREDEG Working Papers 2018-15, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    4. Einy, Ezra & Haimanko, Ori, 2020. "Equilibrium existence in games with a concave Bayesian potential," Games and Economic Behavior, Elsevier, vol. 123(C), pages 288-294.
    5. Ui, Takashi & 宇井, 貴志, 2019. "The Lucas Imperfect Information Model with Imperfect Common Knowledge," Discussion Papers 2019-04, Graduate School of Economics, Hitotsubashi University.
    6. UI, Takashi & 宇井, 貴志, 2015. "Bayesian Nash Equilibrium and Variational Inequalities," Discussion Papers 2015-08, Graduate School of Economics, Hitotsubashi University.
    7. Einy, Ezra & Haimanko, Ori, 2023. "Pure-strategy equilibrium in Bayesian potential games with absolutely continuous information," Games and Economic Behavior, Elsevier, vol. 140(C), pages 341-347.
    8. Brenton Kenkel, 2019. "The efficacy of cheap talk in collective action problems," Journal of Theoretical Politics, , vol. 31(3), pages 370-402, July.
    9. de Martí, Joan & Zenou, Yves, 2015. "Network games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 221-240.
    10. Siegfried Berninghaus & Werner G³th & Hartmut Kliemt, 2003. "Reflections on Equilibrium: Ideal Rationality and Analytic Decomposition of Games," Homo Oeconomicus, Institute of SocioEconomics, vol. 20, pages 257-302.
    11. Satoru Takahashi, 2020. "Non-equivalence between all and canonical elaborations," The Japanese Economic Review, Springer, vol. 71(1), pages 43-57, January.
    12. Gonzalez, Stéphane & Lardon, Aymeric, 2021. "Axiomatic foundations of the core for games in effectiveness form," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 28-38.
    13. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers halshs-01930836, HAL.
    14. Ui, Takashi & Yoshizawa, Yasunori, 2015. "Characterizing social value of information," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 507-535.
    15. Takashi Ui & Stephen Morris, 2020. "Incomplete Information Robustness," Working Papers on Central Bank Communication 019, University of Tokyo, Graduate School of Economics.
    16. David P. Myatt & Chris Wallace, 2008. "On the Sources and Value of Information: Public Announcements and Macroeconomic Performance," Economics Series Working Papers 411, University of Oxford, Department of Economics.
    17. Takashi Ui, 2009. "Bayesian potentials and information structures: Team decision problems revisited," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(3), pages 271-291, September.
    18. Mathevet, Laurent & Taneva, Ina, 2020. "Organized Information Transmission," MPRA Paper 104302, University Library of Munich, Germany.
    19. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
    20. Antonio Jiménez-Martínez, 2014. "Information acquisition interactions in two-player quadratic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 455-485, May.
    21. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    22. Takashi Ui, 2019. "The Lucas Imperfect Information Model with Imperfect Common Knowledge," Working Papers on Central Bank Communication 007, University of Tokyo, Graduate School of Economics.
    23. Takashi Ui, 2020. "The Lucas imperfect information model with imperfect common knowledge," The Japanese Economic Review, Springer, vol. 71(1), pages 85-100, January.

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