Two player statistical game with higher order cumulants

In statistical game, multiple players optimize the distributions of the objective functions through the cost cumulants. This paper extends the use of second, third, and fourth cumulants for stochastic Nash games. For the case of linear system with quadratic cost, the equilibrium solutions are determined. In the process, coupled Riccati equations are found. The higher order statistical game is applied to the control of satellite attitude control application and the results are compared with H_∞ control. The simulation showed that the performance can be manipulated by choosing appropriate parameters. In our case we found that the fourth cumulant case is 26%, 25% and 16% faster than H_∞ control, second cumulant, and third cumulant cases, respectively.