IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v113y2019icp339-355.html
   My bibliography  Save this article

Polyequilibrium

Author

Listed:
  • Milchtaich, Igal

Abstract

Polyequilibrium is a generalization of Nash equilibrium that is applicable to any strategic game, whether finite or otherwise, and to dynamic games, with perfect or imperfect information. It differs from equilibrium in specifying strategies that players do not choose and by requiring an after-the-fact justification for the exclusion of these strategies rather than the retainment of the non-excluded ones. Specifically, for each excluded strategy of each player there must be a non-excluded one that responds at least as well as the first strategy does to every profile of non-excluded strategies of the other players. A particular result (e.g., Pareto efficiency of the payoffs) is said to hold in a polyequilibrium if it holds for all non-excluded profiles. As such a result does not necessarily hold in any Nash equilibrium in the game, the generalization proposed in this work extends the set of justifiable predictions concerning a game's results.

Suggested Citation

  • Milchtaich, Igal, 2019. "Polyequilibrium," Games and Economic Behavior, Elsevier, vol. 113(C), pages 339-355.
    • Handle: RePEc:eee:gamebe:v:113:y:2019:i:c:p:339-355
    DOI: 10.1016/j.geb.2018.09.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825618301556
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2018.09.013?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. Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
    2. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    3. Van Damme, Eric, 2002. "Strategic equilibrium," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 41, pages 1521-1596, Elsevier.
    4. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    5. Vitaly Pruzhansky, 2003. "On Finding Curb Sets in Extensive Games," Tinbergen Institute Discussion Papers 03-098/1, Tinbergen Institute.
    6. Moulin, Herve, 1979. "Dominance Solvable Voting Schemes," Econometrica, Econometric Society, vol. 47(6), pages 1137-1151, November.
    7. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    8. Duggan, John & Le Breton, Michel, 1996. "Dutta's Minimal Covering Set and Shapley's Saddles," Journal of Economic Theory, Elsevier, vol. 70(1), pages 257-265, July.
    9. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    10. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-544, May.
    11. Vitaly Pruzhansky, 2003. "On finding curb sets in extensive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 205-210, December.
    12. Basu, Kaushik, 1994. "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory," American Economic Review, American Economic Association, vol. 84(2), pages 391-395, May.
    Full references (including those not matched with items on IDEAS)

    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. Igal Milchtaich, 2015. "Polyequilibrium," Working Papers 2015-06, Bar-Ilan University, Department of Economics.
    2. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    3. Lensberg, Terje & Schenk-Hoppé, Klaus Reiner, 2021. "Cold play: Learning across bimatrix games," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 419-441.
    4. Burkhard C. Schipper & Hang Zhou, 2022. "Level-k Thinking in the Extensive Form," Working Papers 352, University of California, Davis, Department of Economics.
    5. John Duggan & Michel Le Breton, 2014. "Choice-theoretic Solutions for Strategic Form Games," RCER Working Papers 580, University of Rochester - Center for Economic Research (RCER).
    6. Lavi, Ron & Nisan, Noam, 2015. "Online ascending auctions for gradually expiring items," Journal of Economic Theory, Elsevier, vol. 156(C), pages 45-76.
    7. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    8. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2019. "Comprehensive rationalizability," Games and Economic Behavior, Elsevier, vol. 116(C), pages 185-202.
    9. Carlos Alós-Ferrer & Klaus Ritzberger, 2020. "Reduced normal forms are not extensive forms," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 281-288, October.
    10. R. J. Aumann & J. H. Dreze, 2005. "When All is Said and Done, How Should You Play and What Should You Expect?," Discussion Paper Series dp387, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    11. Geir B. Asheim & Mark Voorneveld & Jörgen W. Weibull, 2016. "Epistemically Robust Strategy Subsets," Games, MDPI, vol. 7(4), pages 1-16, November.
    12. Balkenborg, Dieter & Hofbauer, Josef & Kuzmics, Christoph, 2016. "Refined best reply correspondence and dynamics," Center for Mathematical Economics Working Papers 451, Center for Mathematical Economics, Bielefeld University.
    13. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    15. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.
    16. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    17. Droste, Edward & Kosfeld, Michael & Voorneveld, Mark, 2003. "Best-reply matching in games," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 291-309, December.
    18. Geir B. Asheim & Mark Voorneveld & Jörgen Weibull, 2009. "Epistemically stable strategy sets," Working Papers hal-00440098, HAL.
    19. Ferdinando Colombo, 2003. "The Game Take–or–Play: A Paradox of Rationality in Simultaneous Move Games," Bulletin of Economic Research, Wiley Blackwell, vol. 55(2), pages 195-202, April.
    20. Burkhard Schipper, 2015. "Strategic teaching and learning in games," Working Papers 151, University of California, Davis, Department of Economics.

    More about this item

    Keywords

    Polystrategy; Polyequilibrium; Coarsening of Nash equilibrium; Subgame perfection;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:gamebe:v:113:y:2019:i:c:p:339-355. 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.