Dynamic Games with Perfect Information

In this paper we formulate some easy looking but hard to solve problems from pursuit-evasion game theory. Then we focus on the main problem which, from our point of view, arises in dynamic cooperative games: this is the time-inconsistency of optimal solutions. We propose a system of payments, which we call imputation distribution procedure, that can keep the solution time-consistent when the game develops along the cooperative trajectory. It is shown that if payments are made according to an imputation distribution procedure, the cooperative solution can be achieved as a specially constructed Nash equilibrium in punishment strategies. This brings together noncooperative and cooperative approaches in modern game theory, as cooperation can be supported strategically.