Finding optimal Stackelberg production strategies: How to produce in times of war?

TL;DR

This paper models a Stackelberg game in a military context where a leader allocates resources to maximize production, and a follower aims to destroy it, providing an efficient algorithm to find optimal strategies.

Contribution

It introduces a novel Stackelberg production game model with military applications and presents a linear time algorithm to compute optimal strategies within a specific strategy class.

Findings

Optimal follower strategy identified

Leader's optimal strategy in series-balanced class

Linear time algorithm for strategy computation

Abstract

Inspired by a military context, we study a Stackelberg production game where a country's government, the leader, wants to maximize the production of military assets. The leader does so by allocating his resources among a set of production facilities. His opponent, the follower, observes this allocation and tries to destroy the associated production as much as possible by allocating his destructive resources, for example bombs, among these facilities. In this paper, we identify a follower's optimal strategy. For the leader, we show that an optimal production strategy can be found in the class of so-called seried-balanced strategies. We present a linear time algorithm that finds an optimal strategy in this class.