TY - JOUR
T1 - Probabilistic assignment problem with multi-unit demands
T2 - A generalization of the serial rule and its characterization
AU - Heo, Eun Jeong
N1 - Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2014/10/1
Y1 - 2014/10/1
N2 - 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. Our main result is that the generalized serial rule, which we propose as an adaptation of the serial rule to our setting, is the only rule satisfying sd-efficiency, the sd proportional-division lower-bound, limited invariance, and consistency. Uniqueness persists if we replace the sd proportional-division lower-bound by sd normalized-no-envy, or 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.
AB - 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. Our main result is that the generalized serial rule, which we propose as an adaptation of the serial rule to our setting, is the only rule satisfying sd-efficiency, the sd proportional-division lower-bound, limited invariance, and consistency. Uniqueness persists if we replace the sd proportional-division lower-bound by sd normalized-no-envy, or 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.
KW - Consistency
KW - Limited invariance
KW - Sd normalized-no-envy
KW - Sd proportional-division lower-bound
KW - Sd-efficiency
KW - The generalized serial rule
UR - http://www.scopus.com/inward/record.url?scp=84913540663&partnerID=8YFLogxK
U2 - 10.1016/j.jmateco.2014.08.003
DO - 10.1016/j.jmateco.2014.08.003
M3 - Article
AN - SCOPUS:84913540663
SN - 0304-4068
VL - 54
SP - 40
EP - 47
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
ER -