Differential Games with Random Terminal Instants

Sergey Kostyunin

Faculty of Applied Mathematics, St. Petersburg State University, University pr., 35, Petrodvorets, 198904, St. Petersburg, Russia

Abstract: We investigate a noncooperative differential game with two players. Each player has his own random terminal time. After the first player leaves the game, the remaining one continues and gets the final reward for winning. An example is introduced where two firms compete in extracting a unique nonrenewable resource over time. The optimal feedback strategy, i.e. the optimal extraction rate, is calculated in a closed form.

Keywords: Differential game, random terminal time, Hamilton–Jacobi–Bellman equation.

Language: English