Geodesic
Stable Shapley value in cooperative game of territorial environmental production
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 1, pp. 67-92

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A game-theoretic model of territorial environmental production is studied. The process is modeled as cooperative differential game. The stable mechanism of distribution 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. The perfect Nash equilibrium is found. 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, 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. 
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     author = {Nikolay A. Zenkevich and Nadezhda V. Kozlovskaya},
     title = {Stable {Shapley} value in cooperative game of territorial environmental production},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {67--92},
     publisher = {mathdoc},
     volume = {2},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2010_2_1_a3/}
}
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Nikolay A. Zenkevich; Nadezhda V. Kozlovskaya. Stable Shapley value in cooperative game of territorial environmental production. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 2 (2010) no. 1, pp. 67-92. http://geodesic.mathdoc.fr/item/MGTA_2010_2_1_a3/