An attrition game on an acyclic network

Abstract

This paper deals with noncooperative games in which two players conflict on a network through an attrition phenomenon. The associated problem has a variety of applications, but we model the problem as a military conflict between an attacker and a defender on an acyclic network. The attacker marches from a starting node to a destination node, expecting to keep his initial members untouched during the march. The defender deploys his forces on arcs to intercept the attacker. If the attacker goes through an arc with deployed defenders, the attacker incurs casualties according to Lanchester’s linear law. In this paper, we discuss two games having the number of remaining attackers as the payoff and propose systems of linear programming formulations to derive their equilibrium points. One game is a two-person zero-sum (TPZS) one-shot game with no information and the other is a TPZS game with two stages separated by information acquisition about players’ opponents.

Keywords:

• game theory
• military
• linear programming
• attrition
• network
• interdiction