TY - CHAP

T1 - Integral with respect to non-additive measure in economics

AU - Ozaki, Hiroyuki

PY - 2014

Y1 - 2014

N2 - This chapter surveys the use of non-additive measures in economics, focusing on their use in preference theory. In economics, the risky situation where the probability measure is known and the uncertain situation where even the probability measure is unknown had tended not to be distinguished. This is mainly because of Savage's theorem which states that if an agent complies with some set of behavioral axioms, she may be regarded as trying to maximize the expected utility with respect to some probability measure. This is called subjective expected utility (SEU) theory. However, the plausible and robust preference patterns which cannot be explained by SEU is known. The most famous one among them is Ellsberg's paradox. The attempts to resolve these anomalies by using non-additive measures were initiated by D. Schmeidler and I. Gilboa in 1980's. The main purpose of this chapter is to explain their theories, emphasizing representation theorems by means of non-additive measures. We will see that their models nicely resolve Ellsberg's paradox.

AB - This chapter surveys the use of non-additive measures in economics, focusing on their use in preference theory. In economics, the risky situation where the probability measure is known and the uncertain situation where even the probability measure is unknown had tended not to be distinguished. This is mainly because of Savage's theorem which states that if an agent complies with some set of behavioral axioms, she may be regarded as trying to maximize the expected utility with respect to some probability measure. This is called subjective expected utility (SEU) theory. However, the plausible and robust preference patterns which cannot be explained by SEU is known. The most famous one among them is Ellsberg's paradox. The attempts to resolve these anomalies by using non-additive measures were initiated by D. Schmeidler and I. Gilboa in 1980's. The main purpose of this chapter is to explain their theories, emphasizing representation theorems by means of non-additive measures. We will see that their models nicely resolve Ellsberg's paradox.

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U2 - 10.1007/978-3-319-03155-2_5

DO - 10.1007/978-3-319-03155-2_5

M3 - Chapter

AN - SCOPUS:84958523961

SN - 9783319031545

VL - 310

T3 - Studies in Fuzziness and Soft Computing

SP - 97

EP - 130

BT - Studies in Fuzziness and Soft Computing

PB - Springer Verlag

ER -