Robust Dynamic Cooperative Games

Classical cooperative game theory is no longer a suitable tool for those situations where the values of coalitions are not known with certainty. Recent works address situations where the values of coalitions are modelled by random variables. In this work we still consider the values of coalitions as uncertain, but model them as unknown but bounded disturbances. We do not focus on solving a specific game, but rather consider a family of games described by a polyhedron: each point in the polyhedron is a vector of coalitions’ values and corresponds to a specific game. We consider a dynamic context where while we know with certainty the average value of each coalition on the long run, at each time such a value is unknown and fluctuates within the bounded polyhedron. Then, it makes sense to define “robust��? allocation rules, i.e., allocation rules that bound, within a pre- defined threshold, a so-called complaint vector while guaranteeing a certain average (over time) allocation vector. We also present as motivating example a joint replenishment application.