Cominimum additive operators
AbstractThis 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 InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 43 (2007)
Issue (Month): 2 (February)
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Other versions of this item:
- Atsushi Kajii & Hiroyuki Kojima & Takashi Ui, 2005. "Cominimum Additive Operators," KIER Working Papers, Kyoto University, Institute of Economic Research 601, Kyoto University, Institute of Economic Research.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- D90 - Microeconomics - - Intertemporal Choice - - - General
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