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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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/

[1] Petrosyan L. A., “Ustoichivost reshenii v differentsialnykh igrakh so mnogimi uchastnikami”, Vestn. Leningr. un-ta. Ser. 1, 1977, no. 19(4), 46–52 | Zbl

[2] Petrosyan L. A., Zenkevich N. A., “Printsipy ustoichivoi kooperatsii”, Mat. teoriya igr i eë prilozheniya, 1:1 (2009), 102–117 | MR | Zbl

[3] Borkey P., Leveque F., “Voluntary approaches for environmental protection in the European Union – a survey”, European Environment, 10 (2000), 35–54 | 3.0.CO;2-M class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[4] Demsetz H., “Toward a theory of property rights”, The American Economic Review, 57:2 (1967), 347–359

[5] Dockner E. J., Jorgensen S., van Long N., Sorger G., Differential Games in Economics and Management Science, Cambridge University Press, 2000, 485 pp. | MR | Zbl

[6] Katsoulacos Y., Xepapadeas A., “Environmental policy under oligopoly with endogenous market structure”, Scand. J. of Economics, 97:3 (1995), 411–420 | DOI | Zbl

[7] Nash J. F., “Equilibrium points in $n$-person games”, Proc. Nat. Acad. Sci. USA, 36 (1950), 48–49 | DOI | MR | Zbl

[8] Petrosyan L., Zaccour G., “Time-consistent Shapley value allocation of pollution cost reduction”, Journal of Economic Dynamics and Control, 27 (2003), 381–398 | DOI | MR

[9] Petrosyan L., Kozlovskaya N., “Differential coalitional environmental management game”, Game theory and applications, 14, St. Petersburg State University, Russia, Accepted

[10] Shapley L. S., “A value for $n$-person games”, Contributions to the Theory of Games II, Princeton University Press, Prineton, 1953, 57–69 | MR

[11] Stimming M., “Capital accumulation subject to pollution control: Open-Loop versus feedback investment strategies”, Annals of Operations Research, 88 (1999), 309–336 | DOI | MR | Zbl

[12] Yeung D. W. K., “An irrational-behavior-proofness condition in cooperative differential games”, Intern. J. of Game Theory Rew., 8 (2006), 739–744 | DOI | MR | Zbl