Economic Theory 16, 355–362 (2000) The stand-alone test and decreasing serial cost sharing Jens Leth Hougaard and Lars Thorlund-Petersen Copenhagen Business School, Department of Operations Management, Solbjerg Pl. 3, 2000 Frederiksberg, DENMARK Received: July 29, 1999; revised version: October 4, 1999 Summary. The rule of decreasing serial cost sharing defined in de Frutos [1] over the class of concave cost functions may violate the important stand-alone test. Sufficient conditions for the test to be satisfied are given, in terms of in- dividual rationality as well as coalitional stability. These conditions restrict the shape of the cost function and the distribution of demands. Keywords and Phrases: Serial cost sharing, The stand-alone test, The core. JEL Classification Numbers: D63, D78, C79. 1 Introduction Serial cost sharing has originally been defined in Moulin and Shenker [4] on the domain of increasing cost functions. For convex cost functions, serial cost sharing has strong strategical and ethical properties. Although for concave cost functions the strategical properties of the original serial rule are somewhat weaker, it is shown in Moulin [5] that this rule nevertheless satisfies the important stand-alone test. Recently, as an alternative rule, decreasing serial cost sharing has been defined in de Frutos [1] on the domain of concave cost functions. This reversed serial rule has several nice strategical properties, which mimics those of the original serial rule for convex cost functions. In particular, decreasing serial cost sharing has stronger strategical properties than the original serial rule for concave cost functions (see [1], [5]). On the other hand, the decreasing serial rule has the disadvantage that it sometimes violates the stand-alone test, see [1]. Correspondence to : J.L. Hougaard