Coalitional Stochastic Differential Games for Networks

We consider a networked stochastic cooperative differential game by incorporating two types of networks that allow us to study both the dynamic coupling among decision-makers and their strategic interaction. We study a class of coalitional stochastic differential games by means of the Shapley value to determine how influential the edges of either the dynamic coupling or strategic interaction network are in the minimization of the common cost functional in the differential game. Different from most of the literature where the power index is associated to the decision-makers, here we focus on the power index for the network links. We introduce fairness for the distribution of costs by introducing a network-based power index for the decision-makers.