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.
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