Mean-field interactions among robust dynamic coalitional games with transferable utilities

This paper considers a large number of homogeneous “small worlds” or games. Each small world involves a set of players and a corresponding set of possible coalitions, and is modeled as a dynamic game with transferable utilities (TU), where the characteristic function is a continuous-time stochastic process. Considering that a dynamic TU game can be modeled as a network control problem, the overall system appears as an assembly of a large number of networks subject to mean-field interactions. As a result of such mean-field interactions among small worlds, in each game, a central planner allocates revenues based on the extra reward that a coalition has received up to the current time and the extra reward that the same coalition has received in the other games. We obtain allocation rules that make the grand coalition stable in each game, while guaranteeing consensus on the excesses, in the spirit of inequity aversion. Convergences of allocations and excesses are established via stochastic stability theory.