Serial Rules in a Multi-Unit Shapley-Scarf Market

Abstract

We study generalized Shapley-Scarf exchange markets where each agent is endowed with multiple units of an indivisible and agent-specific good and monetary compensations are not possible. An outcome is given by a circulation which consists of a balanced exchange of goods. We focus on circulation rules that only require as input ordinal preference rankings of individual goods, and agents are assumed to have responsive preferences over bundles of goods. We study the properties of serial dictatorship rules which allow agents to choose either a single good or an entire bundle sequentially, according to a fixed ordering of the agents. We also introduce and explore extensions of these serial dictatorship rules that ensure individual rationality. The paper analyzes the normative and incentive properties of these four families of serial dictatorships and also shows that the individually rational extensions can be implemented with efficient graph algorithms.