http://swrc.ontoware.org/ontology#Article
Cominimum additive operators
en
Choquet integral
comonotonicity
non-additive probabilities
capacities
cooperative games
Kajii Atsushi
Kojima Hiroyuki
Ui Takashi
This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space Omega, which include additivity and comonotonic additivity as extreme cases. Let E subset of 2(Omega) be a collection of subsets of Omega. Two functions x and y on Omega are E-cominimum if, for each E epsilon E, the set of minimizers of x restricted on E and that of y have a common element. An operator I on the set of functions on Omega is E-cominimum additive if I(x + y) = I(x) + I(y) whenever x and y are E-cominimum. The main result characterizes homogeneous S-cominimum additive operators in terms of the Choquet integrals and the corresponding non-additive signed measures. As applications, this paper gives an alternative proof for the characterization of the E-capacity expected utility model of Eichberger and Kelsey [Eichberger, J., Kelsey, D., 1999. E-capacities and the Ellsberg paradox. Theory and Decision 46, 107-140] and that of the multiperiod decision model of Gilboa [Gilboa, I., 1989. Expectation and variation in multiperiod decisions. Econometrica 57, 1153-1169]. (c) 2006 Elsevier B.V. All rights reserved.
Journal of Mathematical Economics
43
2
218-230
2007-02
03044068
info:doi/10.1016/j.jmateco.2006.07.007
NOTICE: This is the author's version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structual formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been to this work since it was submitted for publication.
application/pdf
Elsevier Science SA
postprint