2024/05/01 by E. A. Kolpakova, Kolpakova, Ekaterina
Decision Sciences · #49L25 #49N35 #49N70 #49N75 #91A23 #Analysis of PDEs (math.AP) #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.2405.00371
openalex publication_date 2024/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is concerned with a zero-sum differential game in the case where a payoff is determined by the exit time, that is, the first time when the system leaves the game domain. Additionally, we assume that a part of domain's boundary is a lifeline where the payoff is infinite. Hereby, the examined problem generalizes the well-known time-optimal problem as well as time-optimal problem with lifeline. The main result of the paper relies on the solution to the Direchlet problem for the Hamilton-Jacobi equation associated with the game with exit time. We prove the existence of the value function for examined problem and construct suboptimal feedback strategies under assumption that the associated Dirichlet problem for the Hamilton-Jacobi equation admits a viscosity/minimax solution. Additionally, we derive a sufficient condition of existence result to this Dirichlet problem.