Benefactors and Beneficiaries: The Effects of Giving and Receiving on Cost‐Coalitional Problems

Motivated by supply chain collaborations in practice, we introduce a class of cost-coalitional problems, which are based on a priori information about the cost faced by each agent in each set that it could belong to. Our focus is on problems with decreasingly monotonic coalitional costs. In this class of problems, we study the effects of giving and receiving when there exist players whose participation in an alliance always contributes to the savings of all alliance members (we refer to these players as benefactors), and there also exist players whose cost decreases in such an alliance (we call them beneficiaries). We use linear and quadratic norm cost games to analyze the role played by benefactors and beneficiaries in achieving stability of different cooperating alliances. We consider different notions of stability (the core and the bargaining set) and provide conditions for stability of an all-inclusive alliance of agents which leads to minimum value of total cost incurred by all agents.