The recently defined class of integer programming games (IPG) models situations where multiple self-interested decision makers interact, with their strategy sets represented by a finite set linear constraints together requirements. Many real-world problems can suitably be fit in this class, and hence anticipating IPG outcomes is crucial value for policy regulators. Nash equilibria have been wid...

A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of $$n \Delta $$ on the proximity optimal solutions Integer Linear Programming problem its standard linear relaxation. In this bound, n is number variables $$\Delta denotes maximum absolute values subdeterminants constraint matrix. Hochbaum Shanthikumar, Werman Magagnosc showed that same valid if a more general co...

This paper develops an integer programming approach to two‐sided many‐to‐one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that exists in discrete when the firms' preference profile satisfies total unimodularity condition compatible with various forms complementarities. provide class profiles satisfy this condition.