Abstract Interpretation of Supermodular Games

TL;DR

This paper introduces a novel approach using abstract interpretation to approximate pure strategy Nash equilibria in supermodular games, bridging game theory and static analysis techniques.

Contribution

It extends abstract interpretation theory to handle multivalued functions and applies it to approximate Nash equilibria in supermodular games.

Findings

Provides a method for approximating Nash equilibria

Ensures correctness of approximations within the abstract interpretation framework

Extends abstract interpretation to multivalued functions

Abstract

Supermodular games find significant applications in a variety of models, especially in operations research and economic applications of noncooperative game theory, and feature pure strategy Nash equilibria characterized as fixed points of multivalued functions on complete lattices. Pure strategy Nash equilibria of supermodular games are here approximated by resorting to the theory of abstract interpretation, a well established and known framework used for designing static analyses of programming languages. This is obtained by extending the theory of abstract interpretation in order to handle approximations of multivalued functions and by providing some methods for abstracting supermodular games, in order to obtain approximate Nash equilibria which are shown to be correct within the abstract interpretation framework.