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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.
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    4. 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.
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    6. 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.
    7. 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.
    8. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    9. 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.
    10. 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.
    11. 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.
    12. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    13. 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.
    14. repec:fth:tilbur:9998 is not listed on IDEAS
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    Cited by:

    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.
    2. Brandl, Florian & Brandt, Felix, 0. "An axiomatic characterization of Nash equilibrium," Theoretical Economics, Econometric Society.

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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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