Multi - Cumulant and Non - Inferior Strategies for Multi - Player

The paper presents an extension of cost-cumulant control theory over a finite horizon for a class of two-team pursuit-evasion games wherein the evolution of the states of the game in response to decision strategies selected by pursuit and evasion teams from non-inferior sets of admissible controls is described by stochastic linear differential equation and integral quadratic cost. Since the sum of the aggregate cost functions of two teams is equal to zero, the amount that one team gains is equal to the amount of the other team loses. Both cooperation within each team and competition between the teams presumably exist. A direct dynamic programming approach for the Mayer optimization problem is used to solve for a multi-cumulant and non-inferior based solution when the members in each team measure the states and minimize the first k cumulants of the standard integral-quadratic cost associated with this special class of multi-player pursuit-evasion games.