Differential Search Games with Mobile Hider

In differential search games with a mobile hider of the princess and the monster type formulated by Isaacs, two blind players P, the pursuer, and E, the evader, are initially distributed in a playing space S and may move therein on paths determined by their control variables, P being constrained to move no faster than a given maximum speed. The game terminates at a given time T, and the payoff is the capture probability which P maximizes and E minimizes.Two such games are analyzed; in the first S is a circle, and in the second S is a region of the plane. The game where S is a circle is solved for very general initial relative distributions of the players in S and all termination times T.The game where S is a region of the plane is solved for the equiprobable relative initial distribution of the two players in a region far from the boundary of S relative to the distance that P can travel in time T (that is for situations in which the boundary is sufficiently far away as to make no difference).