Reference functions and solutions to bargaining problems with and without claims

Following an idea due to Thomson (Journal of Economic Theory, 1981, 25: 431–441) we examine the role of reference functions in the axiomatic approach to the solution of bargaining problems with and without claims. A reference function is a means of summarizing essential features of a bargaining problem. Axioms like Independence of Irrelevant Alternatives and Monotonicity are then reformulated with respect to this reference function. Under some weak conditions on the reference function we obtain characterizations of different parametrized classes of solutions. We present several examples of reference functions and thereby recover many well-known solutions to bargaining problems with and without claims.This paper is part of the author’s Ph.D. thesis at Bielefeld University, Germany. The author is particularly grateful to Walter Trockel for his advice and to an associate editor and two referees for their helpful comments. Financial support through a scholarship of the Deutsche Forschungsgemeinschaft (DFG) at the graduate college ‘‘Mathematical Economics’’ is gratefully acknowledged.