Probabilistic Assignment with Multiple Demands: A Generalization and a Characterization of the Serial Rule

Abstract

We study a random assignment problem when each agent has possibly multiple demands on objects. In the case of unitary demands, Bogomolnaia and Moulin (2001) introduce the serial rule and characterize it for three-agent economies. We generalize the model to accommodate the possibility that demands may differ across agents and introduce a generalization of the serial rule. We first present a non-existence result of a rule satisfying sd-efficiency, fairness, and weak sd-strategy-proofness. Based on this negative result, we introduce limited invariance in place of weak sd-strategy-proofness. Our main result is that the generalized serial rule is the only rule satisfying sd-efficiency, the sd proportional division lower bound, limited invariance, and consistency. We can replace the sd proportional division lower bound by sd normalized-no-envy, and consistency by converse consistency, or both. The serial rule in Bogomolnaia and Moulin (2001) is characterized as a special case of our generalized serial rule.

Keywords: the generalized serial rule, sd-efficiency, sd proportional division lower bound, sd normalized-no-envy, limited invariance, consistency, converse consistency, weak sd-strategy-proofness

JEL Classification: C70, D61, D63