Nash equilibria of quasisupermodular games
Lu Yu
TL;DR
The paper investigates the existence and organization of pure Nash equilibria in quasisupermodular games, extending classic results for supermodular games by employing purely order-theoretic methods and weakened continuity notions. It proves an order-theoretic structure theorem for the equilibrium set $E$ under mild assumptions, and a maximum-existence theorem that generalizes prior results to chain-valued payoffs on complete lattices. By leveraging a generalized Veinott framework and transfer-continuity concepts, the work shows that $E$ is a nonempty complete lattice and, under stronger hypotheses, admits a greatest (and sometimes a least) equilibrium obtained through fixed-point arguments (including Tarski). These results unify and extend Milgrom-Shannon, Zhou, and Calciano, broadening the applicability of strategic complementarities to non-numeric payoff structures and providing tools for analyzing economic models with generalized continuity properties.
Abstract
We prove three results on the existence and structure of Nash equilibria for quasisupermodular games. A theorem is purely order-theoretic, and the other two involve topological hypotheses. Our topological results genralize Zhou's theorem (for supermodular games) and Calciano's theorem.