Int J Game Theory 2001) 30:147±165 9999 2001 On the set of Lorenz-maximal imputations in the core of a balanced game Jens Leth Hougaard1, Bezalel Peleg2, Lars Thorlund-Petersen3 1 Institute of Economics, University of Copenhagen, Studiestraede 6, 1455 Copenhagen K., Denmark. E-mail: Jens.Leth.Hougaard@econ.ku.dk) 2 Hebrew University Jerusalem, Center Rationality, Interaction, Decision Theory, Givat-Ram, Feldman Building, 91 904 Jerusalem, ISRAEL 3 Copenhagen Business School, Department of Operations Management, Solbjerg Pl. 3, 2000 Frederiskberg, DENMARK Received: February 1999/Final version: June 2001 Abstract. This paper considers the set of Lorenz-maximal imputations in the core of a balanced cooperative game as a solution concept. It is shown that the Lorenz-solution concept satis®es a number of suitable properties such as desirability, continuity and the reduced game property. Moreover, the paper consideres alternative characterizations where it is shown that Lorenz-fairness is tantamount to the existence of an additive, strictly increasing and concave social welfare function. Finally the paper also provides axiomatic character- izations as well as two examples of application. Key words: Balanced games, the core, Lorenz-maximal imputations. 1. Introduction Consider the set of cooperative games with transferable utility. Following von Neumann and Morgenstern's original notion of stable sets several solution con- cepts have emerged: the Shapley value, the core, the bargaining set, the kernel, the nucleolus etc. This paper will examine the set of Lorenz maximal imputations in the core as a solution concept for balanced cooperative games. Using a solution concept based on the set of Lorenz maximal imputations in the core signals that subject to coalitional stability, egalitarianism is used as a standard of fairness. Hence such a solution concept combines economic rationality among the players with a normative rule of egalitarianism. There are two main characteristics of Lorenz maximal imputations in the core. The ®rst is, obviously, that such imputations are members of the core. Immediately this implies that if the equal split allocation is in the core then it will be the unique Lorenz maximal imputation. In fact, not only is a Lorenz