Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization

We study a probabilistic assignment problem when agents have multi-unit demands for objects. We first introduce two fairness requirements to accommodate different demands across agents. We show that each of these requirements is incompatible with stochastic dominance efficiency (henceforth, we use the prefix “sd” for stochastic dominance) and weak sd-strategy-proofness, unless all agents have unitary demands. We next introduce a new incentive requirement which we call limited invariance. We explore implications of these requirements in combination of consistency or converse consistency.