STABLE COOPERATION UNDER ENVIRONMENTAL CONSTRAINTS

Nadezhda Kozlovskaya () and Nikolay Zenkevich ()
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Nadezhda Kozlovskaya: St. Petersburg University, Universitetski pr. 35, St. Petersburg, 198504, Russia

International Game Theory Review (IGTR), 2010, vol. 12, issue 04, 453-470

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.

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 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219198910002775

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