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Equilibria of the Games in Choice Form

Author

Listed:
  • Anton Stefanescu

    (University of Bucharest)

  • Massimiliano Ferrara

    (University “Mediterranea” of Reggio Calabria)

  • Maria Viorica Stefanescu

    (Academy of Economic Studies)

Abstract

Equilibrium in choice is a solution-concept for noncooperative games defined in a general framework—the game in choice form. There are two leading ideas of the new definition. One is that the players’ preferences need not be explicitly represented, but earlier accepted solution concepts should be formally derived as particular cases. Secondly, the choice of a player need not be a best reply to the strategy combination of the others, if the choices of the other players are motivated for themselves and a best reply does not exist. It is shown that in the present framework are included classical models of game theory, and the new concept extends various known noncooperative solutions. The main technical results of the paper concern the existence of the equilibrium in choice. As particular cases, known results on the existence of classical solutions are found. Thus, our approach can be also seen as a general method for proving the existence of different solutions for noncooperative games.

Suggested Citation

  • Anton Stefanescu & Massimiliano Ferrara & Maria Viorica Stefanescu, 2012. "Equilibria of the Games in Choice Form," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 1060-1072, December.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:3:d:10.1007_s10957-012-0093-7
    DOI: 10.1007/s10957-012-0093-7
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    References listed on IDEAS

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    1. Tan, Kok-Keong & Yu, Jian & Yuan, Xian-Zhi, 1995. "Existence Theorems of Nash Equilibria for Non-cooperative N-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(3), pages 217-222.
    2. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    3. Stefanescu, Anton & Ferrara, Massimiliano, 2006. "Implementation of voting operators," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 315-324, June.
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    Cited by:

    1. Monica Patriche, 2017. "Existence of the Equilibrium in Choice," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 158-171, October.
    2. Carlos Hervés-Beloso & Monica Patriche, 2014. "A Fixed-Point Theorem and Equilibria of Abstract Economies with Weakly Upper Semicontinuous Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 719-736, December.

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