IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v183y2019icp786-822.html
   My bibliography  Save this article

Strategic uncertainty and equilibrium selection in discontinuous games

Author

Listed:
  • Bich, Philippe

Abstract

We introduce the new concept of prudent equilibrium to model strategic uncertainty, and prove it exists in large classes of discontinuous games. When the game is better-reply secure, we show that prudent equilibrium refines Nash equilibrium. In contrast with the current literature, we don't use probabilities to model players' strategies and beliefs about other players' strategies. We provide examples (first-price auctions, location game, Nash demand game, etc.) where prudent equilibrium concept removes most non-intuitive solutions of the game.

Suggested Citation

  • Bich, Philippe, 2019. "Strategic uncertainty and equilibrium selection in discontinuous games," Journal of Economic Theory, Elsevier, vol. 183(C), pages 786-822.
    • Handle: RePEc:eee:jetheo:v:183:y:2019:i:c:p:786-822
    DOI: 10.1016/j.jet.2019.08.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053119300821
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2019.08.001?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 search for a different version of it.

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
    3. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    4. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Post-Print hal-01396183, HAL.
    5. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen, 2010. "Robustness to strategic uncertainty in price competition," SSE/EFI Working Paper Series in Economics and Finance 0726, Stockholm School of Economics, revised 08 Apr 2010.
    6. Bich, Philippe & Laraki, Rida, 2017. "On the existence of approximate equilibria and sharing rule solutions in discontinuous games," Theoretical Economics, Econometric Society, vol. 12(1), January.
    7. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    8. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
    9. Guilherme Carmona, 2011. "Understanding some recent existence results for discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 31-45, September.
    10. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    11. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01337293, HAL.
    12. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    13. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    14. Jean-François Mertens, 2004. "Ordinality in non cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 387-430, June.
    15. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 17-29, September.
    16. Matthew J. Ryan, 2002. "What do uncertainty-averse decision-makers believe?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 47-65.
    17. Carbonell-Nicolau, Oriol, 2011. "On the existence of pure-strategy perfect equilibrium in discontinuous games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 23-48, January.
    18. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen W., 2014. "Robustness to strategic uncertainty," Games and Economic Behavior, Elsevier, vol. 85(C), pages 272-288.
    19. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01396183, HAL.
    20. Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, vol. 2(3), pages 1-22, July.
    21. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    22. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    23. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    24. 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.
    25. 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.
    26. Giuseppe De Marco & Maria Romaniello, 2013. "Games Equilibria and the Variational Representation of Preferences," CSEF Working Papers 336, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    27. 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.
    28. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Working Papers halshs-01337293, HAL.
    29. Mukerji, S., 1995. "A theory of play for games in strategic form when rationality is not common knowledge," Discussion Paper Series In Economics And Econometrics 9519, Economics Division, School of Social Sciences, University of Southampton.
    30. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    31. Stauber, Ronald, 2011. "Knightian games and robustness to ambiguity," Journal of Economic Theory, Elsevier, vol. 146(1), pages 248-274, January.
    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. Frédéric Koessler & Marieke Pahlke, 2023. "Feedback Design in Strategic-Form Games with Ambiguity Averse Players," Working Papers halshs-04039083, HAL.

    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. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Working Papers halshs-01337293, HAL.
    2. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01337293, HAL.
    3. Rabia Nessah, 2022. "Weakly continuous security and nash equilibrium," Theory and Decision, Springer, vol. 93(4), pages 725-745, November.
    4. Oriol Carbonell-Nicolau & Richard McLean, 2013. "Approximation results for discontinuous games with an application to equilibrium refinement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 1-26, September.
    5. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    6. Vincenzo Scalzo, 2016. "Remarks on the existence and stability of some relaxed Nash equilibrium in strategic form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 571-586, March.
    7. Carmona, Guilherme, 2019. "On the existence of limit admissible equilibria in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 81(C), pages 14-21.
    8. 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.
    9. Andersson, Ola & Argenton, Cédric & Weibull, Jörgen W., 2014. "Robustness to strategic uncertainty," Games and Economic Behavior, Elsevier, vol. 85(C), pages 272-288.
    10. 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.
    11. Rabia Nessah, 2013. "Weakly Continuous Security in Discontinuous and Nonquasiconcave Games: Existence and Characterization," Working Papers 2013-ECO-20, IESEG School of Management.
    12. 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.
    13. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    14. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Philippe Bich & Rida Laraki, 2013. "On the Existence of Approximated Equilibria and Sharing-Rule Equilibria in Discontinuous Games," Working Papers hal-00846143, HAL.
    20. János Flesch & Dries Vermeulen & Anna Zseleva, 2021. "Legitimate equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 787-800, December.

    More about this item

    Keywords

    Prudent equilibrium; Nash equilibrium; Refinement; Strategic uncertainty; Better-reply secure; Discontinuous games;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • 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
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    Statistics

    Access and download statistics

    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:jetheo:v:183:y:2019:i:c:p:786-822. 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/622869 .

    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.