An attrition game on a network ruled by Lanchester’s square law
研究攻击方与防御方在网络上的零和消耗战博弈，攻击方选择路径、防御方部署兵力，依据兰彻斯特平方律计算伤亡，提出嵌入非线性规划的数值算法求解均衡。
We consider two-person zero-sum attrition games in which an attacker and a defender are in combat with each other on a network. The attacker marches from a starting node to a destination node, hoping that the initial members survive the march. The defender deploys his forces on arcs in order to intercept the attacker. If the attacker encounters the defender on an arc, the attacker incurs casualties according to Lanchester’s square law. We consider two models: a one-shot game in which the two players have no information about their opponents, and a two-stage game in which both players have some information about their opponents. For both games, the payoff is defined as the number of survivors for the attacker. The attacker’s strategy is to choose a path, and the defender’s is to deploy the defending forces on arcs. We propose a numerical algorithm, in which nonlinear programming is embedded, to derive the equilibrium of the game.