Geodesic
On a exhaustible resource extraction differential game with random terminal instants
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 73-82

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We investigate a noncooperative differential game in which two firms compete in extracting a unique nonrenewable resource over time. The respective times of extraction are random and after the first firm finishes extraction, the remaining one continues and gets the final reward for winning. The expected payoffs for each player are obtained in the standard form for the differential games. The Hamilton–Jacobi–Bellman equations for the feedback information structure are determined. An example is introduced where the optimal feedback strategy, i. e. the optimal extraction rate, is calculated in a closed form. Bibliogr. 12.
Keywords: differential game, exhaustible resources, random terminal time, Hamilton–Jacobi–Bellman equation. 
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     author = {S. Yu. Kostyunin and A. Palestini and E. V. Shevkoplyas},
     title = {On a exhaustible resource extraction differential game with random terminal instants},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a7/}
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S. Yu. Kostyunin; A. Palestini; E. V. Shevkoplyas. On a exhaustible resource extraction differential game with random terminal instants. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2013), pp. 73-82. http://geodesic.mathdoc.fr/item/VSPUI_2013_3_a7/