Integer Programming Games: A Gentle Computational Overview

TL;DR

This paper provides a comprehensive computational overview of Integer Programming Games, focusing on algorithms for computing Nash equilibria in non-cooperative, nonconvex multi-agent optimization scenarios, highlighting theoretical and practical challenges.

Contribution

It offers a systematic review, classification, and taxonomy of algorithms for Nash equilibrium computation in IPGs, including theoretical insights and practical comparisons.

Findings

Classification of algorithms for IPG equilibrium computation

Identification of theoretical and practical challenges

Comparison of Stackelberg and simultaneous IPG solutions

Abstract

In this tutorial, we present a computational overview on computing Nash equilibria in Integer Programming Games ($IPG$s), $i.e.$, how to compute solutions for a class of non-cooperative and nonconvex games where each player solves a mixed-integer optimization problem. $IPG$s are a broad class of games extending the modeling power of mixed-integer optimization to multi-agent settings. This class of games includes, for instance, any finite game and any multi-agent extension of traditional combinatorial optimization problems. After providing some background motivation and context of applications, we systematically review and classify the state-of-the-art algorithms to compute Nash equilibria. We propose an essential taxonomy of the algorithmic ingredients needed to compute equilibria, and we describe the theoretical and practical challenges associated with equilibria computation. Finally, we quantitatively and qualitatively compare a sequential Stackelberg game with a simultaneous $IPG$ to highlight the different properties of their solutions.