Two-person zero-sum game with terminal state constraints

Abstract

In this paper, the discrete-time two-person zero-sum game with terminal state constraints is considered. By applying the variational method, the maximum principle for zero-sum game with terminal constraint is derived along with the forward and backward difference equations (FBDEs). The main contributions of this paper are two-fold. On the one hand, by decoupled solving the FBDEs, the analytical solution to the zero-sum game with terminal state constraint is given. On the other hand, the necessary and sufficient conditions for the reachability of the system are obtained. In this way, the solvability of the zero-sum game with terminal state constraint is re-expressed by the reachability of the system.

Keywords:

• Zero-sum game
• maximum principle
• terminal state constraint
• FBDEs
• reachability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grants 61821004, 62250056, and the Natural Science Foundation of Shandong Province (ZR2021ZD14, ZR2021JQ24).