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The Supercore for Normal Form Games

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  • Iñarra García, María Elena
  • Larrea Jaurrieta, María Concepción
  • Saracho de la Torre, Ana Isabel

Abstract

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.

Suggested Citation

  • Iñarra García, María Elena & Larrea Jaurrieta, María Concepción & Saracho de la Torre, Ana Isabel, 2003. "The Supercore for Normal Form Games," IKERLANAK 2003-04, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  • Handle: RePEc:ehu:ikerla:6501
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    References listed on IDEAS

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    1. Alvin E. Roth, 1976. "Subsolutions and the Supercore of Cooperative Games," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 43-49, February.
    2. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    3. Okada, Akira, 1993. "The Possibility of Cooperation in an n-Person Prisoners' Dilemma with Institutional Arrangements," Public Choice, Springer, vol. 77(3), pages 629-656, November.
    4. Kahn, Charles M. & Mookherjee, Dilip, 1992. "The good, the bad, and the ugly: Coalition proof equilibrium in infinite games," Games and Economic Behavior, Elsevier, vol. 4(1), pages 101-121, January.
    5. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    6. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    7. Greenberg, Joseph, 1989. "Deriving strong and coalition-proof nash equilibria from an abstract system," Journal of Economic Theory, Elsevier, vol. 49(1), pages 195-202, October.
    8. Ko Nishihara, 1997. "A resolution of N -person prisoners' dilemma," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(3), pages 531-540.
    9. Noritsugu Nakanishi, 2001. "On the existence and efficiency of the von Neumann-Morgenstern stable set in a n-player prisoners' dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 291-307.
    10. Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590 Elsevier.
    11. Daniel G. Arce M., 1994. "Stability Criteria for Social Norms with Applications to the Prisoner's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 38(4), pages 749-765, December.
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    Keywords

    individual contingent threat situation; Nash equilibrium; subsolution; Von Neumann; Morgenstern stable set;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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