Stable Group Purchasing Organizations

In this paper, we study the stability of Group Purchasing Organizations (GPOs). GPOs exist in several sectors and benefit its members through quantity discounts and negotiation power when dealing with suppliers. However, despite several obvious benefits, GPOs suffer from member dissatisfaction due to unfair allocations of the accrued savings among its members. We first explore the benefits of allocation rules that are commonly reported as being used in practice. We characterize stable coalitional outcomes when these rules are used and provide conditions under which the grand coalition emerges as a tenable outcome. These conditions are somewhat restrictive. We then propose an allocation mechanism based on the marginal value of a member's contribution and find that this leads to stable GPOs in many scenarios of interest. In this analysis, we look at discount schedules that encompass a large class of practical schedules and analyze cases when purchasing requirements of the members are both exogenous as well as endogenous. We use a concept of stability that allows for players to be farsighted, i.e., players will consider the possibility that once they act (say by causing a defection), another coalition may react, and a third coalition might in turn react, and so on, nullifying their original advantage in making the initial move.