Probabilistic multimodeling in zero-sum differential games

A theory of existence and characterization of equilibria is developed for stochastic zero-sum differential games when the players operate under different (probabilistic) models for the underlying system and measurement processes. The authors identify salient features of such an extended formulation for zero-sum stochastic differential games with noisy measurements, and analyze the equilibria that emerge from possible inconsistent modeling. After a general discussion on the implications of subjective probabilistic modeling on saddle-point equilibria, the authors study the class of zero-sum differential games where the players have a common (noisy) measurement of the state, but different (subjective) statistics on the system measurement noise processes. The author obtains a characterization of the equilibrium solution in the presence of such a discrepancy and studies the structural consistency of the solution and its convergence to the saddle-point solution of the nominal game as the discrepancy becomes (in some norm) vanishingly small.