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An axiomatic characterization of Nash equilibrium

Author

Listed:
  • Brandl, Florian

    (Department of Economics, University of Bonn)

  • Brandt, Felix

    (Department of Computer Science, Technische Universität München)

Abstract

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms:(i) strictly dominant actions are played with positive probability, (ii) if a strategy profile is played in two games, it is also played in every convex combination of these games, and (iii) players can shift probability arbitrarily between two indistinguishable actions, and deleting one of these actions has no effect. Our theorem implies that every equilibrium refinement violates at least one of these axioms. Moreover, every solution concept that approximately satisfies these axioms returns approximate Nash equilibria, even in natural subclasses of games, such as two-player zero-sum games, potential games, and graphical games.

Suggested Citation

  • Brandl, Florian & Brandt, Felix, 2024. "An axiomatic characterization of Nash equilibrium," Theoretical Economics, Econometric Society, vol. 19(4), November.
  • Handle: RePEc:the:publsh:5825
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Game theory; axiomatic characterization; Nash equilibrium;
    All these keywords.

    JEL classification:

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

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