The assortative matching scheme in a survival battle

We consider a battle between two groups D (defenders) and A (attackers). Each group has the same number of agents, but they differ by their abilities. Every agent confronts only one opponent from the other group once in either an all-pay contest or a Tullock contest such that the number of the contests is identical to the number of the agents in each group. The object of group D is to win all the contests in order to survive, or else it will be defeated by group A. We analyze the optimal matching scheme for group D and show that the assortative matching scheme, in which the two agents with the highest ability from each group confront each other, the two agents with the second highest ability from each group confront each other, and so on, is the optimal matching scheme for maximizing group D’s probability to survive the battle.