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Cominimum additive operators

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  • Kajii, Atsushi
  • Kojima, Hiroyuki
  • Ui, Takashi

Abstract

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 \epsilon be a collection of subsets of \omega. Two functions x and y on \omega are \epsilon-cominimum if, for each E \subseteq \epsilon, 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 is E- cominimum additive if I(x+y) = I(x)+I(y) whenever x and y are \epsilon-cominimum. The main result characterizes homogeneous E-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 (1999) and that of the multi-period decision model of Gilboa (1989).

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 43 (2007)
Issue (Month): 2 (February)
Pages: 218-230

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Handle: RePEc:eee:mateco:v:43:y:2007:i:2:p:218-230

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  1. Nouweland, C.G.A.M. van den & Borm, P.E.M. & Tijs, S.H., 1992. "Allocation rules for hypergraph communication situations," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-146635, Tilburg University.
  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 571-87, May.
  3. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, Econometric Society, vol. 57(5), pages 1153-69, September.
  4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 18(2), pages 141-153, April.
  5. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, Springer, vol. 46(2), pages 107-138, April.
  6. Algaba, E. & Bilbao, J.M. & Borm, P.E.M. & Lopez, J.J., 1998. "The position value for union stable systems," Research Memorandum, Tilburg University, Faculty of Economics and Business Administration 768, Tilburg University, Faculty of Economics and Business Administration.
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Cited by:
  1. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, Elsevier, vol. 51(1), pages 1-22, January.
  2. Takashi Ui & Hiroyuki Kojima & Atsushi Kajii, 2011. "The Myerson value for complete coalition structures," Computational Statistics, Springer, Springer, vol. 74(3), pages 427-443, December.

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