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Axiomatic characterizations of solutions for Bayesian games

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

    (Tilburg University, Faculty of Economics)

  • Borm, P.E.M.

    (Tilburg University, Faculty of Economics)

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," Research Memorandum FEW 680, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiurem:b16fc7d9-aee7-4f36-95f2-3b62ed360b21
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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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    Citations

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    Cited by:

    1. Takashi Ui & Stephen Morris, 2020. "Incomplete Information Robustness," Working Papers on Central Bank Communication 019, University of Tokyo, Graduate School of Economics.
    2. 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.
    3. 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.
    4. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic foundations of a unifying concept of the core of games in effectiveness form," Post-Print halshs-01902122, HAL.
    5. 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.
    6. 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.
    7. Mathevet, Laurent & Taneva, Ina, 2020. "Organized Information Transmission," MPRA Paper 104302, University Library of Munich, Germany.
    8. 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.
    9. 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.
    10. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Cowles Foundation Discussion Papers 1629, Cowles Foundation for Research in Economics, Yale University.
    11. UI, Takashi & 宇井, 貴志, 2015. "Bayesian Nash Equilibrium and Variational Inequalities," Discussion Papers 2015-08, Graduate School of Economics, Hitotsubashi University.
    12. 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.
    13. 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.
    14. Brenton Kenkel, 2019. "The efficacy of cheap talk in collective action problems," Journal of Theoretical Politics, , vol. 31(3), pages 370-402, July.
    15. de Martí, Joan & Zenou, Yves, 2015. "Network games with incomplete information," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 221-240.
    16. Ui, Takashi, 2016. "Bayesian Nash equilibrium and variational inequalities," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 139-146.
    17. 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.
    18. Stéphane Gonzalez & Aymeric Lardon, 2018. "Axiomatic Foundations of a Unifying Core," Working Papers 1817, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    19. Satoru Takahashi, 2020. "Non-equivalence between all and canonical elaborations," The Japanese Economic Review, Springer, vol. 71(1), pages 43-57, January.
    20. 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.
    21. 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.
    22. Takashi Ui, 2020. "The Lucas imperfect information model with imperfect common knowledge," The Japanese Economic Review, Springer, vol. 71(1), pages 85-100, January.
    23. Ui, Takashi & Yoshizawa, Yasunori, 2015. "Characterizing social value of information," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 507-535.

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