Multicriteria Minimax Theorem on Two-Person Zero-Sum Dynamic Game Problem (I)

Considering a minimax problem to a two-person zero-sum dynamic game, we establish the total value function of game losses and gains in a stochastic game system. It could perform a minimax theorem. Moreover, we prove that minimax theorem is established by the stochastic space of their strategy spaces for the two-person zero-sum dynamic game under the law of motion. It is also established that the saddle value function exists under certain natural conditions so that the equilibrium point exists in this dynamic game sys- tem. A practical example could be employed to our framework in the context.