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Strategically Supported Cooperation

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    (Faculty of Applied Mathematics, Saint Petersburg University, Universitetskiy pr., 35, Petrodvorets, Saint Petersburg, Russia, 198504, Russia)

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    An n-person differential game Γ(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 α, which is considered as a solution of a cooperative version of the game Γ(x, T - t). Using individual rationality of the imputation α we prove that if in the game Γ(y(s),T - s) along the cooperative trajectory y(s), the solution will be derived from the imputation α with the use of the imputation distribution procedure (IDP), for each given ε > 0 there exists ε-Nash equilibrium in Γ(x, T - t) for which the payoffs of the players in the game will be equal exactly to the components of the imputation α (cooperative outcome). This means that the imputation α is strategically supported by some specially constructed ε-Nash equilibrium in Γ(x, T - t). A similar result is true for a discrete game with perfect information.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 10 (2008)
    Issue (Month): 04 ()
    Pages: 471-480

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    Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:04:p:471-480
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