Game-theoretic control of the object's random jump structure in the class of pure strategies (Q1995339)

Consider a dynamic stochastic game with a random jump structure, which has a finite number of admissible states. The system is controlled by two opponent players, having a finite number of admissible strategies. Besides some a priori information about the underlying dynamic system, the players have information about the probabilities of transition between states. The payoff functions, depending on the state and the controls of the two opponents, are defined by the sums of the expected values of a certain loss function. Having here a non-zero-sum game with incomplete information, without a saddle point, the problem is to find optimal state-feedback controls being deterministic functions of the observations. Based on maxmin-, minmax-criteria for the two players, optimal controls are then constructed by means of stochastic dynamic programming methods. An illustrative example with two states is given.