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, 2012, Volume 5,Pages <nobr>147

This article is cited in 2 papers

A Differential Game-Based Approach to Extraction of Exhaustible Resource with Random Terminal Instants

Sergey Kostyunin^a, Arsen Palestini^b, Ekaterina Shevkoplyas^a

^a Faculty of Applied Mathematics, St. Petersburg University, University pr., 35, Petrodvorets, 198904, St. Petersburg, Russia
^b MEMOTEF, Sapienza University of Rome, Via del Castro Laurenziano 9, 00161 Rome, Italy

Abstract: 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.

Language: English