Int J Game Theory 2001) 29:597±623 9999 2001 Axiomatizations of the core on the universal domain and other natural domains* Yan-An Hwang1, Peter Sudho Èlter2 1 National Dong Hua University, Hualien, Taiwan 2 Institute of Mathematical Economics, University of Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany E-mail: psudhoelter@wiwi.uni-bielefeld.de) Received September 1999/Final version December 2000 Abstract. We prove that the core on the set of all transferable utility games with players contained in a universe of at least ®ve members can be axiomatized by the zero inessential game property, covariance under strategic equivalence, anonymity, boundedness, the weak reduced game property, the converse re- duced game property, and the recon®rmation property. These properties also characterize the core on certain subsets of games, e.g., on the set of totally balanced games, on the set of balanced games, and on the set of superadditive games. Suitable extensions of these properties yield an axiomatization of the core on sets of nontransferable utility games. Key words: TU game, core, kernel; NTU game. 1. Introduction The core on balanced cooperative transferable utility TU) games and on some subclasses can be axiomatized see, e.g., Peleg 1986,1989)). However, in the well-known axiomatizations either nonemptiness or the property of ``coin- cidence with the core on two-person games'' are employed. The assumption that every game under consideration has a nonempty core, is crucial within this context. The characterization of the core presented in this paper does neither refer to balanced games nor does it use one of the axioms just men- tioned. That may be regarded as an advantage over the axiomatizations that are known from literature. With the exception of the ``zero inessential game property'', which requires the solution to be nonempty when applied to * The authors are indebted to Chih Chang and Bezalel Peleg for several helpful conversations and they are grateful to two anonymous referees for some helpful remarks.