A Lattice-Theoretical Optimization Approach to Nash Equilibria in Two-Person Games

17 Pages Posted: 21 Jun 2015 Last revised: 26 Jul 2021

See all articles by Yosuke Yasuda

Yosuke Yasuda

Osaka University - Graduate School of Economics

Date Written: July 24, 2021

Abstract

We propose a functional formulation of Nash equilibrium based on the optimization approach: the set of Nash equilibria, if it is nonempty, is identical to the set of optimizers of a real-valued function. Combining this characterization with lattice theory, we revisit the interchangeability and monotone properties of Nash equilibria in two-person games. We show that existing results on (i) zero-sum games and (ii) supermodular games can be derived in a unified fashion, by the sublattice structure on optimal solutions.

Keywords: Nash equilibrium, optimization, lattice, interchangeability, supermodularity

JEL Classification: C61, C72

Suggested Citation

Yasuda, Yosuke, A Lattice-Theoretical Optimization Approach to Nash Equilibria in Two-Person Games (July 24, 2021). Available at SSRN: https://ssrn.com/abstract=2620861 or http://dx.doi.org/10.2139/ssrn.2620861

Yosuke Yasuda (Contact Author)

Osaka University - Graduate School of Economics ( email )

1-7 Machikaneyama
Toyonaka, Osaka, 560-0043
Japan

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