Abstract
This paper deals with two-person zero-sum (TPZS) games in which two players conflict on a network through an attrition phenomenon. The problem has a variety of applications, but we model the problem as a TPZS game with some attrition between attackers and defenders. The attackers start from a starting node and reach a destination node, expecting to keep their initial members intact. The defenders deploy their forces on arcs to intercept the attackers. If the attackers encounter defenders deployed on an arc, the attackers incur casualties proportional to the number of the deployed defenders. We discuss four games where the attackers or the defenders obtain information of their opponent. The games are two-stage games with a common payoff of the number of surviving attackers. We formulate them into linear programming problems to derive their equilibrium points and evaluate the value of the information acquisitioned in the games.
