More on competition and bargaining in Exchange Economy: a survey and new prospectives

In this paper the author, present a deep survey of analysis of some important properties of an exchange economy core (L. Walras’s classical case). Reintroducing the concept of solution uniformly competitive, introduced in the literature by Stefanescu [13], we show as it, under certain conditions, appears to be equivalent to the concept of competitive set of negotiation (also in weak form). The proofs are obtained starting from definition of cooperative game with nontransferable utility. A new concept extending the classical notion of core is proposed. A competitive bargaining set is a finite collection of allocations, each of them being supported by a coalition, characterized by internal and external stability. Particularly, each core-allocation, together the set of all consumers represents a competitive bargaining set. The existence of the competitive bargaining set is proved for exchange economies if the preferences are represented by continuous monotonic utility functions.