Abstract
This paper studies the problem of assigning n indivisible objects to n agents when each agent consumes one object and monetary transfers are not allowed. Bogomolnaia and Moulin (2001) proved that for n=3, the probabilistic serial mechanism is characterized by the three axioms of ordinal efficiency, envy-freeness, and weak strategy-proofness. We show that this characterization does not extend to problems of arbitrary size; in particular, it does not hold for any n≥5. A number of general characterizations of the probabilistic serial mechanism have been obtained in the recent literature by replacing weak strategy-proofness with various invariance axioms while retaining ordinal efficiency and envy-freeness. We show that weak strategy-proofness is in fact logically independent of all invariance axioms used in these characterizations.
| Original language | English |
|---|---|
| Pages (from-to) | 56-62 |
| Number of pages | 7 |
| Journal | Mathematical Social Sciences |
| Volume | 90 |
| DOIs | |
| Publication status | Published - 2017 Nov 1 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Social Sciences(all)
- Psychology(all)
- Sociology and Political Science
Cite this
On characterizations of the probabilistic serial mechanism involving incentive and invariance properties. / Kesten, Onur; Kurino, Morimitsu; Ünver, M. Utku.
In: Mathematical Social Sciences, Vol. 90, 01.11.2017, p. 56-62.Research output: Contribution to journal › Article
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TY - JOUR
T1 - On characterizations of the probabilistic serial mechanism involving incentive and invariance properties
AU - Kesten, Onur
AU - Kurino, Morimitsu
AU - Ünver, M. Utku
PY - 2017/11/1
Y1 - 2017/11/1
N2 - This paper studies the problem of assigning n indivisible objects to n agents when each agent consumes one object and monetary transfers are not allowed. Bogomolnaia and Moulin (2001) proved that for n=3, the probabilistic serial mechanism is characterized by the three axioms of ordinal efficiency, envy-freeness, and weak strategy-proofness. We show that this characterization does not extend to problems of arbitrary size; in particular, it does not hold for any n≥5. A number of general characterizations of the probabilistic serial mechanism have been obtained in the recent literature by replacing weak strategy-proofness with various invariance axioms while retaining ordinal efficiency and envy-freeness. We show that weak strategy-proofness is in fact logically independent of all invariance axioms used in these characterizations.
AB - This paper studies the problem of assigning n indivisible objects to n agents when each agent consumes one object and monetary transfers are not allowed. Bogomolnaia and Moulin (2001) proved that for n=3, the probabilistic serial mechanism is characterized by the three axioms of ordinal efficiency, envy-freeness, and weak strategy-proofness. We show that this characterization does not extend to problems of arbitrary size; in particular, it does not hold for any n≥5. A number of general characterizations of the probabilistic serial mechanism have been obtained in the recent literature by replacing weak strategy-proofness with various invariance axioms while retaining ordinal efficiency and envy-freeness. We show that weak strategy-proofness is in fact logically independent of all invariance axioms used in these characterizations.
UR - http://www.scopus.com/inward/record.url?scp=85009288388&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85009288388&partnerID=8YFLogxK
U2 - 10.1016/j.mathsocsci.2016.11.005
DO - 10.1016/j.mathsocsci.2016.11.005
M3 - Article
AN - SCOPUS:85009288388
VL - 90
SP - 56
EP - 62
JO - Mathematical Social Sciences
JF - Mathematical Social Sciences
SN - 0165-4896
ER -