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A game-theoretic model of pollution control with asymmetric time horizons
Contributions to game theory and management, Tome 9 (2016), pp. 170-179 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the contribution a problem of pollution control is studied within the game-theoretic framework (Kostyunin et al., 2013; Gromova and Plekhanova, 2015; Shevkoplyas and Kostyunin, 2011). Each player is assumed to have certain equipment whose functioning is related to pollution control. The $i$-th player's equipment may undergo an abrupt failure at time $T_i$. The game lasts until any of the players' equipment breaks down. Thus, the game duration is defined as $T=\min(T_1,\dots, T_n)$, where $T_i$ is the time instant at which the $i$-th player stops the game. We assume that the time instant of the $i$-th equipment failure is described by the Weibull distribution. According to Weibull distribution form parameter, we consider different scenarios of equipment exploitation, where each of player can be in “an infant”, “an adult” or “an aged” stage. The cooperative 2-player game with different scenarios is studied.
Keywords: differential game, cooperative game, pollution control, random duration, Weibull distribution. 
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     author = {Ekaterina V. Gromova and Anna V. Tur and Lidiya I. Balandina},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2016_9_a4/}
}
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Ekaterina V. Gromova; Anna V. Tur; Lidiya I. Balandina. A game-theoretic model of pollution control with asymmetric time horizons. Contributions to game theory and management, Tome 9 (2016), pp. 170-179. http://geodesic.mathdoc.fr/item/CGTM_2016_9_a4/

[1] Breton M., Zaccour G., Zahaf M., “A Differential Game of Joint Implementation of Environmental Projects”, Automatica, 41:10 (2005), 1737–1749 | DOI | MR | Zbl

[2] Kostyunin S. Yu., Palestini A., Shevkoplyas E. V., “On a exhaustible resource extraction differential game with random terminal instants”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 2013, no. 3, 73–82

[3] Gromova E., Plekhanova K., “A differential game of pollution control with participation of developed and developing countries”, Contributions to Game Theory and Management, 8 (2015), 64–83 | MR

[4] Kostyunin S., Shevkoplyas E., “On simplification of integral payoff in the differential games with random duration”, Vestnik St. Petersburg University. Ser. 10, 2011, no. 4, 47–56

[5] Shevkoplyas E., Kostyunin S., “Modeling of Environmental Projects under Condition of a Random Time Horizon”, Contributions to Game Theory and Management, 4 (2011), 447–459 | MR | Zbl

[6] Petrosjan L. A., Murzov N. V., “Game-theoretic problems of mechanics”, Litovsk. Mat. Sb., 6 (1966), 423–433 (in Russian) | MR | Zbl

[7] Yeung D. W. K., Petrosjan L. A., Cooperative Stochastic Differential Games, Springer, New-York–Heidelberg–London, 2006, 242 pp. | MR | Zbl

[8] Weibull W., “A statistical distribution function of wide applicability”, J. Appl. Mech.-Trans. ASME, 18:3 (1951), 293–297 | Zbl