An axiomatic characterization of Nash equilibrium

Florian Brandl () and Felix Brandt ()
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Florian Brandl: Department of Economics, University of Bonn
Felix Brandt: Department of Computer Science, Technische Universität München

Theoretical Economics, 2024, vol. 19, issue 4

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.

Keywords: Game theory; axiomatic characterization; Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2024-11-14
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Citations: View citations in EconPapers (3)

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