The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon

Tatyana Balas and Anna Tur ()
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Tatyana Balas: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia
Anna Tur: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia

Mathematics, 2023, vol. 11, issue 2, 1-13

Abstract: A differential game with random duration is considered. The terminal time of the game is a random variable settled using a composite distribution function. Such a scenario occurs when the operating mode of the system changes over time at the appropriate switching points. On each interval between switchings, the distribution of the terminal time is characterized by its own distribution function. A method for solving such games using dynamic programming is proposed. An example of a non-renewable resource extraction model is given, where a solution of the problem of maximizing the total payoff in closed-loop strategies is found. An analytical view of the optimal control of each player and the optimal trajectory depending on the parameters of the described model is obtained.

Keywords: differential game; random time horizon; composite distribution function; non-renewable resource extraction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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