IDEAS home Printed from https://ideas.repec.org/a/spr/etbull/v7y2019i2d10.1007_s40505-018-0157-4.html
   My bibliography  Save this article

Equilibria in games with weak payoff externalities

Author

Listed:
  • Takuya Iimura

    (Tokyo Metropolitan University)

  • Toshimasa Maruta

    (Nihon University)

  • Takahiro Watanabe

    (Tokyo Metropolitan University)

Abstract

Ania (J Econ Behav Organ 65:472–488, 2008) shows that in the class of symmetric games with weak payoff externalities, symmetric Nash equilibria are equivalent to symmetric evolutionary equilibria (Schaffer in J Econ Behav Organ 12:29–45, 1989). We introduce a notion of a game with partial weak payoff externalities. We show that the class of games with partial weak payoff externalities includes most of previously known classes of games in which the equivalence prevails. We also establish a number of pure strategy Nash equilibrium existence results for a game with weak payoff externalities, and for a class of games that includes games with partial weak payoff externalities. The results include, in particular, the existence of pure strategy Nash equilibrium in some finite games.

Suggested Citation

  • Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2019. "Equilibria in games with weak payoff externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 245-258, December.
    • Handle: RePEc:spr:etbull:v:7:y:2019:i:2:d:10.1007_s40505-018-0157-4
    DOI: 10.1007/s40505-018-0157-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40505-018-0157-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40505-018-0157-4?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. Marx, Leslie M. & Swinkels, Jeroen M., 2000. "Order Independence for Iterated Weak Dominance," Games and Economic Behavior, Elsevier, vol. 31(2), pages 324-329, May.
    2. Hehenkamp, Burkhard & Possajennikov, Alex & Guse, Tobias, 2010. "On the equivalence of Nash and evolutionary equilibrium in finite populations," Journal of Economic Behavior & Organization, Elsevier, vol. 73(2), pages 254-258, February.
    3. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
    4. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
    5. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
    6. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 29-45, August.
    7. 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.
    8. Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2020. "Two-person pairwise solvable games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 385-409, June.
    9. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, 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. Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2020. "Two-person pairwise solvable games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 385-409, June.
    2. Takuya Iimura, 2020. "Unilaterally competitive games with more than two players," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 681-697, September.

    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. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
    2. Konrad, Kai A. & Morath, Florian, 2016. "Bargaining with incomplete information: Evolutionary stability in finite populations," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 118-131.
    3. Gu, Yiquan & Hehenkamp, Burkhard & Leininger, Wolfgang, 2019. "Evolutionary equilibrium in contests with stochastic participation: Entry, effort and overdissipation," Journal of Economic Behavior & Organization, Elsevier, vol. 164(C), pages 469-485.
    4. Leininger, Wolfgang & Moghadam, Hamed M., 2014. "Evolutionary Stability in Asymmetric Oligopoly. A Non-Walrasian Result," Ruhr Economic Papers 497, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    5. Robert Philipowski, 2016. "Spiteful behavior can make everybody better off," Evolutionary and Institutional Economics Review, Springer, vol. 13(1), pages 113-116, June.
    6. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
    7. Hamed Markazi Moghadam, 2020. "Price and non-price competition in an oligopoly: an analysis of relative payoff maximizers," Journal of Evolutionary Economics, Springer, vol. 30(2), pages 507-521, April.
    8. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
    9. 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.
    10. Erik Balder, 2011. "An equilibrium closure result for discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 47-65, September.
    11. Ania, Ana B. & Wagener, Andreas, 2009. "The Open Method of Coordination (OMC) as an Evolutionary Learning Process," Hannover Economic Papers (HEP) dp-416, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    12. Pavlo Prokopovych, 2010. "Domain L-Majorization and Equilibrium Existence in Discontinuous Games," Discussion Papers 31, Kyiv School of Economics, revised May 2011.
    13. Thomas Vallée & Murat Yıldızoğlu, 2013. "Can They Beat the Cournot Equilibrium? Learning with Memory and Convergence to Equilibria in a Cournot Oligopoly," Computational Economics, Springer;Society for Computational Economics, vol. 41(4), pages 493-516, April.
    14. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    15. Wolfgang Leininger & Hamed Moghadam, 2014. "Evolutionary Stability in Asymmetric Oligopoly. A Non-Walrasian Result," Ruhr Economic Papers 0497, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    16. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    17. Thomas W. L. Norman, 2021. "Evolutionary stability in the generalized second-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 235-250, February.
    18. 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.
    19. Wei He & Xiang Sun & Yeneng Sun & Yishu Zeng, 2021. "Characterization of equilibrium existence and purification in general Bayesian games," Papers 2106.08563, arXiv.org.
    20. Hehenkamp, Burkhard & Possajennikov, Alex & Guse, Tobias, 2010. "On the equivalence of Nash and evolutionary equilibrium in finite populations," Journal of Economic Behavior & Organization, Elsevier, vol. 73(2), pages 254-258, February.

    More about this item

    Keywords

    Existence of equilibrium; Evolutionary equilibrium; Weak payoff externalities; Weakly unilaterally competitive games; Weakly competitive games; Potential games;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary 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:spr:etbull:v:7:y:2019:i:2:d:10.1007_s40505-018-0157-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.