Reformulation of Nash Equilibrium with an Application to Interchangeability

14 Pages Posted: 21 Jun 2015 Last revised: 9 May 2016

See all articles by Yosuke Yasuda

Yosuke Yasuda

Osaka University - Graduate School of Economics

Date Written: May 9, 2016

Abstract

We propose a reformulation of Nash equilibrium based on optimization approach: the set of Nash equilibria, if it is nonempty, is identical to the set of optimizers of a real-valued function, which connects the equilibrium problem to the optimization problem. Incorporating this characterization into lattice theory, we study the interchangeability of Nash equilibria, and show that existing results on two-person (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, interchangeability, lattice, supermodularity

JEL Classification: C61, C72

Suggested Citation

Yasuda, Yosuke, Reformulation of Nash Equilibrium with an Application to Interchangeability (May 9, 2016). 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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