Saddle point conditions for a class of stochastic dynamical games with imperfect information

Nonlinear dynamical games are considered in which one player has full (causal) information on the state and the opponent´s measurements and control, while the other one only has partial, possibly noise-corrupted, state information. A dynamic-programming-like algorithm in an extended space is given that, when successful, yields, a saddle point, usually in mixed strategies. This result is used to provide an equilibrium in safe strategies for the case in which both players are restricted to imperfect state information