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On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information

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  • Prokopovych, Pavlo
  • Yannelis, Nicholas C.

Abstract

This paper develops a new approach to investigating equilibrium existence in first-price auctions with many asymmetric bidders whose types are affiliated and valuations are interdependent and not necessarily strictly increasing in own type. We begin with studying a number of continuity-related properties of the model, which are used, in conjunction with tieless single crossing and H-convexity, to establish the existence of monotone approximate interim equilibria. Then we provide two sets of sufficient conditions for the game to have a sequence of monotone approximate equilibria whose limit points are pure-strategy Bayesian-Nash equilibria.

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  • Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jetheo:v:184:y:2019:i:c:s0022053118306501
    DOI: 10.1016/j.jet.2019.07.012
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    Cited by:

    1. Idione Meneghel & Rabee Tourky, 2019. "On the Existence of Equilibrium in Bayesian Games Without Complementarities," Cowles Foundation Discussion Papers 2190r2, Cowles Foundation for Research in Economics, Yale University, revised Mar 2020.
    2. Oriol Carbonell-Nicolau, 2021. "Equilibria in infinite games of incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 311-360, June.
    3. Idione Meneghel & Rabee Tourky, 2019. "On the Existence of Equilibrium in Bayesian Games Without Complementarities," Cowles Foundation Discussion Papers 2190r, Cowles Foundation for Research in Economics, Yale University, revised Nov 2019.
    4. Oriol Carbonell-Nicolau, 2021. "Perfect equilibria in games of incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1591-1648, June.
    5. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    6. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    7. Wei He, 2022. "Discontinuous stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 827-858, June.
    8. Idione Meneghel & Rabee Tourky, 2019. "On The Existence of Equilibrium In Bayesian Games Without Complementarities," ANU Working Papers in Economics and Econometrics 2019-669, Australian National University, College of Business and Economics, School of Economics.
    9. Pavlo Prokopovych & Nicholas C. Yannelis, 2022. "On nondegenerate equilibria of double auctions with several buyers and a price floor," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 625-654, April.
    10. Idione Meneghel & Rabee Tourky, 2019. "On the Existence of Equilibrium in Bayesian Games Without Complementarities," Cowles Foundation Discussion Papers 2190, Cowles Foundation for Research in Economics, Yale University.
    11. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.

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    More about this item

    Keywords

    First-price auction; Payoff security; Monotone equilibrium; Generalized convexity;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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