IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v132y2022icp448-462.html
   My bibliography  Save this article

Invariant equilibria and classes of equivalent games

Author

Listed:
  • Allison, Blake A.
  • Bagh, Adib
  • Lepore, Jason J.

Abstract

We consider classes of games for a fixed set of players with fixed strategy sets. For such classes, we analyze and develop the concept of invariance, which is satisfied when the set of Nash equilibria and corresponding equilibrium payoffs are identical for each payoff function within the class. We introduce the condition superior payoff matching, which requires that at any given strategy profile, each player can match her highest payoff near that strategy profile across all games within that class. If a specific game satisfies superior payoff matching, then its equilibria are invariant within a class of games with smaller sets of discontinuities. This condition can be used to prove existence of Nash equilibrium in games that are not quasiconcave or better reply secure.

Suggested Citation

  • Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2022. "Invariant equilibria and classes of equivalent games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 448-462.
    • Handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:448-462
    DOI: 10.1016/j.geb.2022.01.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825622000173
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2022.01.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Ettore Damiano & Li Hao, 2008. "Competing Matchmaking," Journal of the European Economic Association, MIT Press, vol. 6(4), pages 789-818, June.
    3. Michael Baye & Dan Kovenock & Casper Vries, 2012. "Contests with rank-order spillovers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 315-350, October.
    4. Simon, Leo K & Zame, William R, 1990. "Discontinuous Games and Endogenous Sharing Rules," Econometrica, Econometric Society, vol. 58(4), pages 861-872, July.
    5. Page, Frank Jr. & Monteiro, Paulo K., 2003. "Three principles of competitive nonlinear pricing," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 63-109, February.
    6. Matthew O. Jackson & Jeroen M. Swinkels, 2005. "Existence of Equilibrium in Single and Double Private Value Auctions," Econometrica, Econometric Society, vol. 73(1), pages 93-139, January.
    7. Dan Kovenock & Brian Roberson, 2018. "The Optimal Defense Of Networks Of Targets," Economic Inquiry, Western Economic Association International, vol. 56(4), pages 2195-2211, October.
    8. Manolis Galenianos & Philipp Kircher, 2012. "On The Game‐Theoretic Foundations Of Competitive Search Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 1-21, February.
    9. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 573-585, June.
    10. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    11. Carmona, Guilherme & Fajardo, José, 2009. "Existence of equilibrium in common agency games with adverse selection," Games and Economic Behavior, Elsevier, vol. 66(2), pages 749-760, July.
    12. Peters, Michael, 2007. "The pre-marital investment game," Journal of Economic Theory, Elsevier, vol. 137(1), pages 186-213, November.
    13. Carmona, Guilherme & Podczeck, Konrad, 2018. "Invariance of the equilibrium set of games with an endogenous sharing rule," Journal of Economic Theory, Elsevier, vol. 177(C), pages 1-33.
    14. Pavlo Prokopovych, 2011. "On equilibrium existence in payoff secure games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 5-16, September.
    15. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    16. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    17. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    18. Lebrun, Bernard, 1996. "Existence of an Equilibrium in First Price Auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(3), pages 421-443, April.
    19. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    20. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
    21. Michele Piccione & Ran Spiegler, 2012. "Price Competition Under Limited Comparability," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(1), pages 97-135.
    22. Matthew O. Jackson & Leo K. Simon & Jeroen M. Swinkels & William R. Zame, 2002. "Communication and Equilibrium in Discontinuous Games of Incomplete Information," Econometrica, Econometric Society, vol. 70(5), pages 1711-1740, September.
    23. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2018. "Sufficient conditions for weak reciprocal upper semi-continuity in mixed extensions of games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 99-107.
    24. Duggan, John, 2007. "Equilibrium existence for zero-sum games and spatial models of elections," Games and Economic Behavior, Elsevier, vol. 60(1), pages 52-74, July.
    25. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    26. Carmona, Guilherme & Podczeck, Konrad, 2018. "The conditions in the existence results for discontinuous games by Reny and by Simon and Zame are incomparable," Games and Economic Behavior, Elsevier, vol. 111(C), pages 16-19.
    27. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
    28. Subhasish M. Chowdhury, 2017. "The All‐Pay Auction with Nonmonotonic Payoff," Southern Economic Journal, John Wiley & Sons, vol. 84(2), pages 375-390, October.
    29. Paulo Monteiro & Frank Page, 2008. "Catalog competition and Nash equilibrium in nonlinear pricing games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 34(3), pages 503-524, March.
    30. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2022. "Invariant equilibria and classes of equivalent games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 448-462.
    31. Blake Allison & Jason Lepore, 2016. "Price Competition with Decreasing Returns-to-Scale: A General Model of Bertrand-Edgeworth Duopoly," Working Papers 1607, California Polytechnic State University, Department of Economics.
    32. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    33. Adib Bagh & Alejandro Jofre, 2006. "Reciprocal Upper Semicontinuity and Better Reply Secure Games: A Comment," Econometrica, Econometric Society, vol. 74(6), pages 1715-1721, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Allison, Blake A. & Bagh, Adib & Lepore, Jason J., 2022. "Invariant equilibria and classes of equivalent games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 448-462.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Rabia Nessah, 2022. "Weakly continuous security and nash equilibrium," Theory and Decision, Springer, vol. 93(4), pages 725-745, November.
    3. Zhiwei Liu & Nicholas C. Yannelis, 2013. "On Discontinuous Games with Asymmetric Information," Economics Discussion Paper Series 1318, Economics, The University of Manchester.
    4. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    5. 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).
    6. Prokopovych, Pavlo & Yannelis, Nicholas C., 2014. "On the existence of mixed strategy Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 87-97.
    7. Monteiro, Paulo K. & Page Jr., Frank H., 2009. "Endogenous mechanisms and Nash equilibrium in competitive contracting games," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 664-678, September.
    8. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Documents de travail du Centre d'Economie de la Sorbonne 12040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717135, HAL.
    10. Philippe Bich & Rida Laraki, 2013. "On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00846143, HAL.
    11. Philippe Bich & Rida Laraki, 2013. "On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous Games," Working Papers hal-00846143, HAL.
    12. Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers 2013-ECO-20, IESEG School of Management.
    13. Tian, Guoqiang, 2015. "On the existence of equilibria in games with arbitrary strategy spaces and preferences," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 9-16.
    14. Scalzo, Vincenzo, 2020. "Doubly Strong Equilibrium," MPRA Paper 99329, University Library of Munich, Germany.
    15. Philippe Bich & Rida Laraki, 2012. "A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games," Post-Print halshs-00717135, HAL.
    16. Carmona, Guilherme & Podczeck, Konrad, 2018. "Invariance of the equilibrium set of games with an endogenous sharing rule," Journal of Economic Theory, Elsevier, vol. 177(C), pages 1-33.
    17. 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.
    18. Philip J. Reny, 2016. "Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 553-569, March.
    19. Philippe Bich & Rida Laraki, 2014. "On the Existence of Approximate Equilibria and Sharing Rule Solutions in Discontinuous Games," Working Papers hal-01071678, HAL.
    20. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:448-462. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.