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An axiomatization of the Nash equilibrium concept

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  • Voorneveld, Mark

Abstract

For strategic games, the Nash equilibrium concept is axiomatized using three properties: (i) if the difference between two games is ‘strategically irrelevant’, then their solutions are the same; (ii) if a player has a strategy with a constant payoff, this player need not settle for less in any solution of the game; (iii) if all players agree that a certain strategy profile is optimal, then this strategy profile is a solution of the game.

Suggested Citation

  • Voorneveld, Mark, 2019. "An axiomatization of the Nash equilibrium concept," Games and Economic Behavior, Elsevier, vol. 117(C), pages 316-321.
    • Handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:316-321
    DOI: 10.1016/j.geb.2019.07.011
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    References listed on IDEAS

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    1. Mark Voorneveld & Peter Borm & Freek Van Megen & Stef Tijs & Giovanni Facchini, 1999. "Congestion Games And Potentials Reconsidered," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 283-299.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    3. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    4. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    5. Peleg, Bezalel & Potters, Jos A M & Tijs, Stef H, 1996. "Minimality of Consistent Solutions for Strategic Games, in Particular for Potential Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 81-93, January.
    6. Peleg, Bezalel & Tijs, Stef, 1996. "The Consistency Principle for Games in Strategic Forms," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 13-34.
    7. Norde, Henk & Potters, Jos & Reijnierse, Hans & Vermeulen, Dries, 1996. "Equilibrium Selection and Consistency," Games and Economic Behavior, Elsevier, vol. 12(2), pages 219-225, February.
    8. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    9. repec:fth:tilbur:9998 is not listed on IDEAS
    10. Giovanni Facchini & Freek van Megen & Peter Borm & Stef Tijs, 1997. "Congestion Models And Weighted Bayesian Potential Games," Theory and Decision, Springer, vol. 42(2), pages 193-206, March.
    11. Patrone, F. & Pieri, G. & Tijs, S.H. & Torre, A., 1996. "On Consistent Solutions for Strategic Games," Other publications TiSEM 07b489e5-dff2-45d0-bd65-1, Tilburg University, School of Economics and Management.
    12. Peleg, Bezalel & Sudholter, Peter, 1997. "An Axiomatization of Nash Equilibria in Economic Situations," Games and Economic Behavior, Elsevier, vol. 18(2), pages 277-285, February.
    13. Voorneveld, Mark, 2010. "The possibility of impossible stairways: Tail events and countable player sets," Games and Economic Behavior, Elsevier, vol. 68(1), pages 403-410, January.
    14. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
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    1. Norde, Henk & Voorneveld, Mark, 2019. "Feasible best-response correspondences and quadratic scoring rules," SSE Working Paper Series in Economics 2019:2, Stockholm School of Economics.

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    More about this item

    Keywords

    Nash equilibrium; Axiomatization; Solution concept;
    All these keywords.

    JEL classification:

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

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