N player Nash cumulant games

In stochastic game theory, the mean of a player´s cost function has played a prominent role as a performance index. However, the mean is just one of many other cumulants. In fact, it is the first cumulant, with the second being the variance. The objective of this paper is to begin an N-player, higher order cumulant, stochastic differential Nash game. The problem is defined for a class of nonlinear systems with non- quadratic costs. Then sufficient conditions for the equilibrium solutions are developed. Lastly, for the case of linear systems with quadratic cost functions, the equilibrium solutions are determined with coupled Riccati equations.