STRATEGICALLY SUPPORTED COOPERATION

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

International Game Theory Review (IGTR), 2008, vol. 10, issue 04, 471-480

Abstract: Ann-person differential gameΓ(x, T-t)with independent motions from the initial statexand with prescribed durationT - tis considered. Suppose thaty(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 payoffV(x, T - t; N)according to the imputation α, which is considered as a solution of a cooperative version of the gameΓ(x, T - t). Using individual rationality of the imputation α we prove that if in the gameΓ(y(s),T - s)along the cooperative trajectoryy(s), the solution will be derived from the imputation α with the use of the imputation distribution procedure (IDP), for each givenε > 0there exists ε-Nash equilibrium inΓ(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.

JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0219198908002059

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