Nash-equilibria and N-fold integer programming

TL;DR

This paper explores the existence of generalized Nash-equilibria in integer programming games and links them to N-fold integer programming, providing complexity results for solving these problems.

Contribution

It establishes the existence of generalized Nash-equilibria in integer programming games and connects them to N-fold integer programming, with new complexity insights.

Findings

Generalized Nash-equilibria always exist in the studied setting.

Nash-equilibria are related to optimal solutions of N-fold integer programs.

Polynomial time complexity results are established for solving these problems.

Abstract

Inspired by a paper of R. W. Rosenthal, we investigate generalized Nash-equilibria of integer programming games. We show that generalized Nash-equilibria always exist and are related to an optimal solution of a so-called N-fold integer program. This link allows us to establish some polynomial time complexity results about solving this optimization problem and its inverse counter-part.