2023-03-29T02:37:09Zhttps://ynu.repo.nii.ac.jp/?action=repository_oaipmhoai:ynu.repo.nii.ac.jp:000020272022-07-04T05:53:51Z00316:00317
Cominimum additive operatorsengChoquet integralcomonotonicitynon-additive probabilitiescapacitiescooperative gameshttp://hdl.handle.net/10131/3087Journal ArticleKajii, AtsushiKojima, HiroyukiUi, TakashiThis 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 Economics4322182302007-0203044068info:doi/10.1016/j.jmateco.2006.07.007NOTICE: 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/pdfauthorhttps://ynu.repo.nii.ac.jp/?action=repository_action_common_download&item_id=2027&item_no=1&attribute_id=20&file_no=1Elsevier Science SApostprint2016-09-15