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Equilibrium Existence In Games With A Concave Bayesian Potential

Author

Listed:
  • Ezra Einy

    (BGU)

  • Ori Haimanko

    (BGU)

Abstract

We establish existence of a pure-strategy Bayesian Nash equilibrium in Bayesian games that have a continuous and concave potential at all states of nature, without assuming absolute continuity of information. As an application, we show that Bayesian Nash equilibrium exists in many well-known games that have semi-quadratic payoffs (including Bertrand and Cournot oligopolies with linear demand), for general information structures.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Ezra Einy & Ori Haimanko, 2019. "Equilibrium Existence In Games With A Concave Bayesian Potential," Working Papers 1911, Ben-Gurion University of the Negev, Department of Economics.
    • Handle: RePEc:bgu:wpaper:1911
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    File URL: http://in.bgu.ac.il/en/humsos/Econ/Workingpapers/1911.pdf
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    References listed on IDEAS

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    1. Yann Bramoull? & Rachel Kranton & Martin D'Amours, 2014. "Strategic Interaction and Networks," American Economic Review, American Economic Association, vol. 104(3), pages 898-930, March.
    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. Einy, Ezra & Haimanko, Ori & Moreno, Diego & Shitovitz, Benyamin, 2010. "On the existence of Bayesian Cournot equilibrium," Games and Economic Behavior, Elsevier, vol. 68(1), pages 77-94, January.
    4. He, Wei & Sun, Yeneng, 2019. "Pure-strategy equilibria in Bayesian games," Journal of Economic Theory, Elsevier, vol. 180(C), pages 11-49.
    5. Raith, Michael, 1996. "A General Model of Information Sharing in Oligopoly," Journal of Economic Theory, Elsevier, vol. 71(1), pages 260-288, October.
    6. , & ,, 2017. "Bayesian games with a continuum of states," Theoretical Economics, Econometric Society, vol. 12(3), September.
    7. 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.
    8. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    9. Balder, Erik J & Yannelis, Nicholas C, 1993. "On the Continuity of Expected Utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(4), pages 625-643, October.
    10. John W. Mamer & Kenneth E. Schilling, 1986. "A Zero-Sum Game with Incomplete Information and Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 627-631, November.
    11. 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.
    12. 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.
    13. 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.
    14. Roy Radner & Robert W. Rosenthal, 1982. "Private Information and Pure-Strategy Equilibria," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 401-409, August.
    15. 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.
    16. Ziv Hellman, 2012. "A Game with No Bayesian Approximate Equilibria," Discussion Paper Series dp615, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    17. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    18. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    19. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2008. "Uniform Continuity of the Value of Zero-Sum Games with Differential Information," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 552-560, August.
    20. Hellman, Ziv, 2014. "A game with no Bayesian approximate equilibria," Journal of Economic Theory, Elsevier, vol. 153(C), pages 138-151.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Bayesian games; Bayesian potential; equilibrium existence; con- cave payo¤s; absolute continuity; information structures;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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