Contested Logistics: A Game-Theoretic Approach

TL;DR

This paper models contested logistics as a two-player zero-sum game on graphs, introducing a sophisticated framework that accounts for adversarial disruptions, multiple transport modes, and demand satisfaction, with a practical solver demonstrated on real-world data.

Contribution

It introduces a novel game-theoretic model for contested logistics, incorporating multiple transport modes and adversarial disruptions, along with a scalable double-oracle solver.

Findings

The proposed method scales to large real-world maps.

Modeling adversary capabilities improves logistics planning.

The double-oracle solver effectively finds approximate equilibria.

Abstract

We introduce Contested Logistics Games, a variant of logistics problems that account for the presence of an adversary that can disrupt the movement of goods in selected areas. We model this as a large two-player zero-sum one-shot game played on a graph representation of the physical world, with the optimal logistics plans described by the (possibly randomized) Nash equilibria of this game. Our logistics model is fairly sophisticated, and is able to handle multiple modes of transport and goods, accounting for possible storage of goods in warehouses, as well as Leontief utilities based on demand satisfied. We prove computational hardness results related to equilibrium finding and propose a practical double-oracle solver based on solving a series of best-response mixed-integer linear programs. We experiment on both synthetic and real-world maps, demonstrating that our proposed method scales to reasonably large games. We also demonstrate the importance of explicitly modeling the capabilities of the adversary via ablation studies and comparisons with a naive logistics plan based on heuristics.