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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
    9. Walker, Mark, 1977. "On the existence of maximal elements," Journal of Economic Theory, Elsevier, vol. 16(2), pages 470-474, December.
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    Cited by:

    1. 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.
    2. 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.

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    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

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