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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Paper provided by Kyoto University, Institute of Economic Research in its series KIER Working Papers with number
601.
Find related papers by JEL classification: 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 and Growth - - - General
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