An attrition game with multiple start and destination points

摘要

This paper deals with an attrition game on a combat network, where attackers depart from multiple start nodes heading to multiple destination nodes and defenders deploy a limited number of members on arcs to intercept the attackers. Due to conflicts between the attackers and the deployed defenders, both players incur casualties or attrition on arcs. The attackers aim to bring as many members as possible to destination nodes while the defenders desires to minimize the number of surviving attackers. For the two-person zero-sum (TPZS) attrition game, we propose linear programming formulations to derive an optimal attacker's strategy of their attack paths and an optimal defender's strategy of deployment on arcs.