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Stable Cooperation Under Environmental Constraints

Author

Listed:
  • NADEZHDA KOZLOVSKAYA

    (St. Petersburg University, Universitetski pr. 35, St. Petersburg, 198504, Russia)

  • NIKOLAY ZENKEVICH

    (St. Petersburg University, Volkhovski per. 1-3, St. Petersburg, 199004, Russia)

Abstract

A game-theoretic model of territorial environmental production under Cournot competition is studied. The process is modeled as cooperative differential game. The stable distribution mechanism of the common cooperative benefit among players is proposed. We proved that the cooperative total stock of accumulated pollution is strictly less then the pollution under Nash equilibrium for the whole duration of the game. We design a stable Shapley value as a cooperative solution, which is time-consistent. The Shapley value is also strategic stable and satisfies the irrational-behavior-proofness condition. The numerical example is given.

Suggested Citation

  • Nadezhda Kozlovskaya & Nikolay Zenkevich, 2010. "Stable Cooperation Under Environmental Constraints," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 453-470.
    • Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:04:n:s0219198910002775
    DOI: 10.1142/S0219198910002775
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    Keywords

    Differential game; differential cooperative game; dynamic programming; Hamilton-Jacobi-Bellman equation; Shapley value; Nash equilibrium; perfect equilibrium; stability of cooperative solution; time-consistency; strategic stability; irrational-behavior-proofness condition; 49N70; 91A12;
    All these keywords.

    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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