Seminar Abstract

yThe law of iterated Choquet expectation by transformed
  probabilities and threshold information partitionsz

------------------------------
Speaker: ¬ˆδ“c L—Y

Affiliation: “Œ‹ž‘εŠw‘εŠw‰@ ŒoΟŠwŒ€‹†‰Θ

Date and Time: 2002. 7.11(Thu), 2:00 - 3:30 p.m.iš ŽžŠΤ‚Ι’ˆΣj

Place: 3F1223išκŠ‚Ι’ˆΣj

Chair: Šˆδ ŒϊŽu

------------------------------
Abstract: 

This paper analyzes the situations in which there are not risks but
uncertainty in the sense of Schmeidler (1989). We show that when the
probability capacity is represented by a transformation of a probability
measure and the update rule is f-Bayesian (Gilboa and Schmeidler (1993))

with a threshold information partition, the Arrow-Pratt measure of this
function (along with the sign of the second-order derivative) determines
the relation between the folding-back and the one-shot Choquet
expectations.

Especially, we show that an equality of two expectations holds for any
threshold information partitions if and only if the Arrow-Pratt measure
is constant, which extends the law of iterated expectation to the case
of non-additive probability and is the counterproposal to Yoo (1991)'s
result.

Further, we consider two cases of more "accurate'' information
structures. One is to increase the number of thresholds and the other 
is to increase the number of iterations. We show that in the former, 
the folding-back expectation approaches the one-shot expected value, 
whereas it approaches the minimum value of the function in the latter 
with descending information resolution.