Serial cost sharing in multidimensional contexts

Abstract

The Serial Cost Sharing Rule was originally conceived for situations where the demands of agents pertain to a homogeneous private good, produced by an unreplicable technology. In this context, it is endowed with a variety of desirable equity and coherency properties. This paper investigates the extension of this rule to the context where agents request many goods that may be public, private or specific to some of them, where aggregation of demands may be very general and where demands may have to be scaled in a non-proportional way, more precisely along paths, in order to compute cost shares. We propose the Path Serial Rule to treat these general problems and we explore its properties and characteristics. Some properties are transposed directly from the single good to the general context. Other properties must be weakened by requiring that they hold only on the paths along which demands must be scaled when needed. This is the case of the serial principle, which we show is incompatible with the basic equal treatment of equals. The resulting weaker Path Serial Principle characterizes the Path Serial Rule together with the Equal Treatment of Equivalent Demands in terms of stand alone costs, a stronger form of Equal Treatment of Equals.