Geodesic
On the conditions on the integral payoff function in the games with random duration
Contributions to game theory and management, Tome 10 (2017), pp. 94-99.

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In this paper we consider the problem of the existence of the integral payoff in the differential games with random duration when the random time is defined on the infinite time interval. We present an example of a game with random duration, a game-theoretic model of the development of non-renewable resources.
Keywords: differential games, random duration, environment, pollution control. 
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Ekaterina V. Gromova; Anastasiya P. Malakhova; Anna V. Tur. On the conditions on the integral payoff function in the games with random duration. Contributions to game theory and management, Tome 10 (2017), pp. 94-99. http://geodesic.mathdoc.fr/item/CGTM_2017_10_a7/

[1] Aseev S. M., Kryazhimskiy A. V., “The maximum Pontryagin principle and problems of optimal economic growth”, Tr. MIAN, 257, Nauka, M., 2007, 3–271 (in Russian) | MR

[2] Boukas E. K., Haurie A., Michel P., “An Optimal Control Problem with a Random Stopping Time”, Journal of optimization theory and applications, 64:3 (1990), 471–480 | DOI | MR | Zbl

[3] Breton M., Zaccour G., Zahaf M., “A differential game of joint implementation of environmental projects”, Automatica, 41:10 (2005), 1737–1749 | DOI | MR | Zbl

[4] Dockner E., Jorgensen S., Long N. V., Sorger G., Differential Games in Economics and Management Science, Cambridge University Press, Cambridge, 2000 | MR | Zbl

[5] Gromova E. V., Lopez-Barrientos Jose Daniel, “A differential game model for the extraction of non renewable resources with random initial times”, Contributions to Game Theory and Management, 8 (2015), 58–-63 | MR

[6] Kostyunin S., Shevkoplyas E., “On simplification of integral payoff in differential games with random duration”, Vestnik S. Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 4 (2011), 47-–56

[7] Marin-Solano J., Shevkoplyas E. V., “Non-constant discounting and differential games with random time horizon”, Automatica, 47:12 (2011), 2626–2638 | DOI | MR | Zbl

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

[9] Petrosjan L. A., Shevkoplyas E. V., “Cooperative Solutions for Games with Random Duration”, Game Theory and Applications, v. IX, Nova Science Publishers, 2003, 125–139 | MR | Zbl

[10] Shevkoplyas E. V., “Optimal Solutions in Differential Games with Random Duration”, Journal of Mathematical Sciences, 189:6 (2014), 715–722 | DOI | MR