Multi-cumulant and pareto solutions for tactics change prediction and performance analysis in stochastic multi-team noncooperative games

Abstract

New solution concepts, called the multi-cumulant Pareto Nash and minimax strategies, are proposed for quadratic decision problemsquadratic decision problems where multiple teams of decision makers are interested in strategies that not only ensure cooperation within each team and competition among different teams but also provide noncooperative teams the capability of assessing team performance and predicting tactics via complete statistical descriptions. Analytical expressions for higher-order statistics associated with strategy selection and performance assessment as well as closed-form feedback Nash equilibrium Nash equilibrium feedback Nash equilibrium and minimax solutions to the special linear-quadratic class of stochastic multi-team gamesstochastic multi-team games are also presented. The capability to shape the probability density function of the team probability density space probability density function performance measure is possible because not only is the first performance statistic considered as in the special case of the statistical control finite linear combination linear-quadratic-gaussian problem, but also some finite linear combinations of other performance statistics are included. probability density space variance In all decision strategies developed here, the decision feedback gains are probability density space skewness explicitly dependent upon the “information” statistics which are then used to directly target the uncertainty of team performance and decision laws. statistical control performance distribution It is concluded that the need to account for the reduction of performance uncertainty gives rise to the interaction between dual decision control functions: reducing uncertainty analysis confidence limits uncertainty and exercising control. As the result, the certainty probability density space mean equivalence property is no longer available for the class of statistical control design freedom statistical control problems considered here.