An n-person differential game Î(x, T-t) with independent motions from the initial state x and with prescribed duration T - t is considered. Suppose that y(s) is the cooperative trajectory maximizing the sum of players' payoffs. Suppose also that before starting the game players agree to divide the joint maximal payoff V(x, T - t; N) according to the imputation Î±, which is considered as a solution of a cooperative version of the game Î(x, T - t). Using individual rationality of the imputation Î± we prove that if in the game Î(y(s),T - s) along the cooperative trajectory y(s), the solution will be derived from the imputation Î± with the use of the imputation distribution procedure (IDP), for each given Îµ > 0 there exists Îµ-Nash equilibrium in Î(x, T - t) for which the payoffs of the players in the game will be equal exactly to the components of the imputation Î± (cooperative outcome). This means that the imputation Î± is strategically supported by some specially constructed Îµ-Nash equilibrium in Î(x, T - t). A similar result is true for a discrete game with perfect information.
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