Geodesic
A Differential Game-Based Approach to Extraction of Exhaustible Resource with Random Terminal Instants
Contributions to game theory and management, Tome 5 (2012), pp. 147-155

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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. An example is introduced where the optimal feedback strategy, i.e. the optimal extraction rate, is calculated in a closed form.
Keywords: Differential game, exhaustible resources, random terminal time, Hamilton–Jacobi–Bellman equation. 
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     author = {Sergey Kostyunin and Arsen Palestini and Ekaterina Shevkoplyas},
     title = {A {Differential} {Game-Based} {Approach} to {Extraction} of {Exhaustible} {Resource} with {Random} {Terminal} {Instants}},
     journal = {Contributions to game theory and management},
     pages = {147--155},
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     volume = {5},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2012_5_a14/}
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Sergey Kostyunin; Arsen Palestini; Ekaterina Shevkoplyas. A Differential Game-Based Approach to Extraction of Exhaustible Resource with Random Terminal Instants. Contributions to game theory and management, Tome 5 (2012), pp. 147-155. http://geodesic.mathdoc.fr/item/CGTM_2012_5_a14/