Econometrica: Sep 1986, Volume 54, Issue 5

Implicit Mean Value and Certainty Equivalence

https://doi.org/0012-9682(198609)54:5<1197:IMVACE>2.0.CO;2-V
p. 1197-1206

Peter C. Fishburn

This paper considers a generalized mean value m (p) defined implicitly for a probability measure p on the reals as the unique y for which @?(x,y) dp (x) = ? where @? is skew-symmetric and strictly increasing in its first argument. Conditions on m that are necessary and sufficient for the implicit characterization are given and its relationship to certainty equivalence is discussed.

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