A problem of guarding a territory with two invaders and two defenders

摘要

In this paper, a problem of guarding a territory with two defenders and two invaders is formulated and investigated. The favorable regions of the players are introduced to analyze this problem qualitatively by dividing the playing space intoseveral regions. First we consider the possibility whether both invaders are capable of entering the territory successfully. If this is not possible, then we consider the possibility whether any one of the invaders is capable of entering the territory, in which case the distance between the territory and the invader not entering the territory is chosen as the payoff. If this is not the case, we consider the sum of the distances between two invaders and the territory as the payoff.