Mixed serial cost sharing

Abstract

A new serial cost sharing rule, called mixed serial cost sharing, is defined on the class of cost functions which equal a sum of an increasing convex and increasing concave function. This rule is based on a particular decomposition principle known as complementary-slackness decomposition and it coincides with the original serial rule of Moulin and Shenker (1992) [Moulin, H., Shenker, S., 1992. Serial cost sharing. Econometrica 60, 1009–1037] and the reversed serial rule of de Frutos (1998) [de Frutos, M.A., 1998. Decreasing serial cost sharing under economies of scale. Journal of Economic Theory 79, 245–275] if the cost function is convex or concave, respectively. The rule and its decomposition are characterized by three properties and the vector of payments is compared with existing cost sharing rules with respect to economic inequality measurement.