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Reconfirming the Prenucleolus

Dept. of Agriculture Economics and Management, The Hebrew University of Jerusalem, P.O. Box 12, Rehovot, 76100, Israel, and Dept. of Mathematics, The Open University of Israel, 16 Klaussner Street, P.O.B. 39382, Ramat Aviv, Tel Aviv, 61392, Israel
Department of Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
orshan{at}agri.huji.ac.il
psu{at}sam.sdu.dk

By means of an example, it is shown that the prenucleolus is not the only minimal solution that satisfies nonemptiness, Pareto optimality, covariance, the equal treatment property, and the reduced game property, even if the universe of players is infinite. This example also disproves a conjecture of Gurvich et al. (1994). As a second result, we prove that the prenucleolus is axiomatized by nonemptiness, covariance, the equal treatment property, and the reconfirmation property, provided the universe of players is infinite.

Key Words: Prenucleolus; game theory
History: Received: September 12, 2001; revision received: March 18, 2002;revision received: September 26, 2002;