TY - JOUR
T1 - An improvement to Jensen's inequality and its application to mating market clearing when paternity is uncertain
AU - Bethmann, Dirk
N1 - Funding Information:
This research is supported by a Korea University Grant ( K1602581 ). I am very grateful to two reviewers for their constructive and valuable comments. Jaeil Cho has provided research assistance. All remaining errors are my own.
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/1
Y1 - 2018/1
N2 - Jensen's inequality can be tightened in the context of discrete random variables. The suggested new inequality coincides with Jensen's inequality only when the expected value of the random variable is an integer, in all other cases the inequality is tighter than Jensen's. This improvement is used to derive a welfare result in the context of a mating market where male agents are exposed to paternal uncertainty. It is shown that social welfare is highest when paternity is certain, a result that cannot be obtained when relying on Jensen's inequality.
AB - Jensen's inequality can be tightened in the context of discrete random variables. The suggested new inequality coincides with Jensen's inequality only when the expected value of the random variable is an integer, in all other cases the inequality is tighter than Jensen's. This improvement is used to derive a welfare result in the context of a mating market where male agents are exposed to paternal uncertainty. It is shown that social welfare is highest when paternity is certain, a result that cannot be obtained when relying on Jensen's inequality.
UR - http://www.scopus.com/inward/record.url?scp=85029542632&partnerID=8YFLogxK
U2 - 10.1016/j.mathsocsci.2017.08.004
DO - 10.1016/j.mathsocsci.2017.08.004
M3 - Article
AN - SCOPUS:85029542632
SN - 0165-4896
VL - 91
SP - 71
EP - 74
JO - Mathematical Social Sciences
JF - Mathematical Social Sciences
ER -