Modeling the Optimal Coalition Structure Using the Core Solution Concept

Coalition formation is an important step towards developing the social welfare by improving the performance. This is pursued in two main research streams: (i) algorithmic approaches to achieve the optimal coalition structure and (ii) cooperative game theory to distribute the coalition payoff based on fairness and stability criteria. The aim of this paper is to integrate the strengths of the two approaches in order to achieve an optimal and stable coalition structure. The main innovation of the paper is using mathematical modeling to incorporates stability condition in a set partitioning problem through core solution concept to overcome decentralized procedures of coalition formation and payoff distribution. A numerical example is used to investigate the performance of overlapping and non-overlapping optimal coalition structure models. The results show that cooperation leads to improve social welfare. This improvement has an ascending trend with a decreasing slope and does not change after increasing the upper limit of players allowed to join the coalition to the certain extent. This is due to several reasons which prevent players to form grand coalition and suggests that, to form large coalitions, one should compare achieved gains with the managerial complexities and the increased costs of coordination and communication between players.