Approximating the Value of Zero-Sum Differential Games with Linear Payoffs and Dynamics

Approximating the Value of Zero-Sum Differential Games with Linear Payoffs and Dynamics

Kuipers, Jeroen (Universiteit Maastricht)
Schoenmakers, Gijs (Universiteit Maastricht)
Staňková, K. (TU Delft Transport and Logistics)

2023

We consider two-player zero-sum differential games of fixed duration, where the running payoff and the dynamics are both linear in the controls of the players. Such games have a value, which is determined by the unique viscosity solution of a Hamilton–Jacobi-type partial differential equation. Approximation schemes for computing the viscosity solution of Hamilton–Jacobi-type partial differential equations have been proposed that are valid in a more general setting, and such schemes can of course be applied to the problem at hand. However, such approximation schemes have a heavy computational burden. We introduce a discretized and probabilistic version of the differential game, which is straightforward to solve by backward induction, and prove that the solution of the discrete game converges to the viscosity solution of the partial differential equation, as the discretization becomes finer. The method removes part of the computational burden of existing approximation schemes.

Differential games
Stochastic games
Viscosity solutions

http://resolver.tudelft.nl/uuid:5c2b5d2a-c901-4d5f-a8fa-ee60da45d1bd

https://doi.org/10.1007/s10957-023-02236-x

0022-3239

Journal of Optimization Theory and Applications, 198 (1), 332-346

Institutional Repository

journal article

© 2023 Jeroen Kuipers, Gijs Schoenmakers, K. Staňková