Ž . GAMES AND ECONOMIC BEHAVIOR 24, 142171 1998 ARTICLE NO. GA970603 Axiomatizations of Game Theoretical Solutions for One-Output Cost Sharing Problems Peter Sudholter* ¨ Institute of Mathematical Economics, Uni  ersity of Bielefeld, 33501 Bielefeld, Germany Received February 6, 1996 Cost sharing rules can be obtained by considering solution concepts on the associated cost games. The Shapley rule, nucleolus rule, and antinucleolus rule commonly satisfy ‘‘covariance under strategical equivalence.’’ Covariance, together with ‘‘equal treatment of equals’’ and either additivity or consistency, characterize the Shapley rule. The nucleolus rules are axiomatized analogously by changing the definition of the ‘‘reduced cost sharing problem’’ adequately. In the case of concave cost functions the nucleolus satisfies a strong version of consistency and the antinucleolus rule is a core selector. Cost functions for which the proposed game theoretical solutions coincide with average cost pricing are characterized by a simple functional equation. Journal of Economic Literature Classification Numbers: C71, D24.  1998 Academic Press Key Words: cost sharing problem and rule; game; solution concept; Shapley value; nucleolus; average cost pricing. INTRODUCTION The problem how to allocate the total production cost of a single homogeneous good is discussed in this paper. A cost function C, i.e. a nondecreasing function on the nonnegative reals which intersects the origin, is used to model the production costs depending on the demanded Ž . quantity. Here Cy should be interpreted as the cost for producing y units of the good. If the agents or players in a finite group N possess the production technology and agent i has demand q , then the question how i Ž . to divide the total cost C Ý q among the players is answered in i  N i general by proposing any cost sharing rule. Several applications occur in Ž . the literature see, e.g., Shenker, 1989, 1990 . A cost sharing rule assigns an allocation to any cost sharing problem Ž . N,C, q , where q is the demand profile of the agents in N, and C is the * E-mail: PSudhoelter@Wiwi.Uni-Bielefeld.de. 142 0899-825698 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.