Coordinated equilibria and a technique for solving differential games (Q2388061)

The paper is concerned with the notion of the so-called ``coordinated'' equilibrium for conflict and program dynamical systems described by differential equations. The proposed modification of the weakest equilibrium permits one to obtain a necessary existence condition for such equilibria in a form similar to necessary optimality conditions for variational problems. On the basis of necessary conditions for coordinated equilibria there is suggested an effective method for finding arbitrary equilibria in differential games with arbitrary many participants. A few theorems are proved using which one can state the iterative procedure of ``generation'' of a family of new equilibria. The proposed techniques is demonstrated by examples. The first contains a game problem with three participants (as factories) in the class of pure strategies, taking only two values. The second example presents a zero-sum two-person differential game, where the participants try to minimize and to maximize the same payoff function.