Computing core allocations in cooperative games with an application to cooperative procurement

Cooperative game theory defines several concepts for distributing outcome shares in a cooperative game with transferable utilities. One of the most famous solution concepts is the core which defines a set of outcome allocations that are stable such that no coalition has an incentive to leave the grand coalition. In this paper we propose a general procedure to compute a core element (or to detect that no core allocation exists) which is based on mathematical programming techniques. The procedure proposed in this paper can be applied to a wide class of cooperative games where the characteristic function is given by the optimum objective function value of a complex optimization problem. For cooperative procurement, which is an example from the field of supply chain management where some literature on the core concept already exists, we prove the applicability and provide computational results to demonstrate that games with 150 players can be handled.