ABSTRACT

Pure bargaining problems with transferable utility are considered. By associating a quasi-additive cooperative game with each one of them, a Shapley rule for this class of problems is derived from the Shapley value for games. The analysis of this new rule includes axiomatic characterizations and a comparison with the proportional rule which gives rise to a strong criticism on this classical rule. Next, we consider pure bargaining problems endowed with a coalition structure such that each union is given its own utility. In this context we use the Shapley rule in order to assess the main options available to the agents: individual behavior, cooperative behavior, isolated union behavior, and bargaining union behavior. The latter two respectively recall the treatment given by Aumann-Drèze and Owen to cooperative games with a coalition structure. A numerical example illustrates the procedure. We provide criteria to compare any pair of behaviors for each agent, introduce and axiomatically characterize a modified Shapley rule, and determine its natural domain, that is, the set of problems where the bargaining union behavior is the best option for all agents.