Ratio Game on a Network

摘要

This paper was originally motivated by a military problem where one side plants mines on a network of roads while the other side clears them in an extended conflict. The two-person zero-sum game considered here is a possible model. The essential features of the game are that the payoff on each segment of the selected path depends only on the ratio of the two sides' allocations of effort, and that the total payoff is a sum over the arcs of that path. We solve the game, presenting mathematical programs for the two sides. One side uses a mixed strategy, while the other does not.