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Strategically Supported Cooperation

Author

Listed:
  • LEON PETROSYAN

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

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.

Suggested Citation

  • Leon Petrosyan, 2008. "Strategically Supported Cooperation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 471-480.
    • Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:04:n:s0219198908002059
    DOI: 10.1142/S0219198908002059
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    Cited by:

    1. Parilina, Elena M. & Zaccour, Georges, 2022. "Payment schemes for sustaining cooperation in dynamic games," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    2. Elena Parilina & Georges Zaccour, 2016. "Strategic Support of Node-Consistent Cooperative Outcomes in Dynamic Games Played Over Event Trees," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-16, June.

    More about this item

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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