TY - JOUR
T1 - Additive representations on a simplex
AU - Qin, Wei zhi
AU - Rommeswinkel, Hendrik
N1 - Funding Information:
This work was financially supported by the Center for Research in Econometric Theory and Applications (Grant No. 109-L900-203 ) from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan, and by the Ministry of Science and Technology (MOST), Taiwan , under Grant Nos. 109-2634-F-002-045 , 104-2410-H-002-239-MY2 , and 110-2410-H-002-229-MY2 .
Publisher Copyright:
© 2022
PY - 2022/12
Y1 - 2022/12
N2 - We characterize additive representations on subsets of product spaces with an empty interior such as simplexes and certain homeomorphisms thereof. Previously, all additive representation theorems only applied to spaces in which any coordinate can be changed without changing any of the other coordinates. We identify a novel preference condition that is necessary and sufficient for the existence of additive representations. Our results provide, for instance, a characterization of utilitarianism on the Pareto frontier of a cake division problem.
AB - We characterize additive representations on subsets of product spaces with an empty interior such as simplexes and certain homeomorphisms thereof. Previously, all additive representation theorems only applied to spaces in which any coordinate can be changed without changing any of the other coordinates. We identify a novel preference condition that is necessary and sufficient for the existence of additive representations. Our results provide, for instance, a characterization of utilitarianism on the Pareto frontier of a cake division problem.
KW - Additive Separability
KW - Preferences
KW - Simplex
KW - Utilitarianism
KW - Utility representation
UR - http://www.scopus.com/inward/record.url?scp=85141961447&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85141961447&partnerID=8YFLogxK
U2 - 10.1016/j.jmateco.2022.102769
DO - 10.1016/j.jmateco.2022.102769
M3 - Article
AN - SCOPUS:85141961447
SN - 0304-4068
VL - 103
JO - Journal of Mathematical Economics
JF - Journal of Mathematical Economics
M1 - 102769
ER -