Abstract
AbstractThis chapter investigates Pareto optimality in infinite horizon stochastic differential games. Employing the equivalent description of Pareto optimality, necessary conditions for the existence of Pareto solutions are presented under certain assumption on the Lagrange multiplier set. Furthermore, a condition is introduced to guarantee that the above assumption is established for the LQ case. In addition, the sufficient conditions for a control to be Pareto efficient are put forward in terms of the necessary conditions, a convexity condition as well as a transversality condition. For the LQ situation, the characterization of Pareto-efficient strategies and Pareto solutions are also studied. If the system is mean-square stabilizable, then the solvability of the related SARE provides a sufficient condition under which Pareto-efficient strategies are equivalent to the weighted sum optimal controls and all Pareto solutions can be derived based on the solutions of an introduced GALE.
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