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Generalized neo‐additive capacities and updating
Author(s) -
Eichberger Jürgen,
Grant Simon,
Lefort JeanPhilippe
Publication year - 2012
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2012.00189.x
Subject(s) - axiom , consistency (knowledge bases) , mathematical economics , core (optical fiber) , choquet integral , independence (probability theory) , bayesian probability , conditional independence , certainty , mathematics , econometrics , set (abstract data type) , regular polygon , economics , computer science , statistics , discrete mathematics , artificial intelligence , telecommunications , geometry , programming language , fuzzy logic
This paper shows that, for Choquet expected utility preferences, the axioms consquentialism, state independence and conditional certainty equivalent consistency under updating characterise a family of capacities, which we call Generalized Neo‐Additive Capacities (GNAC). This family contains as special cases, among others, neo‐additive capacities as introduced by Chateauneuf, Eichberger, and Grant, Hurwicz capacities, and ɛ ‐contaminations. Moreover, we will show that the convex version of a GNAC is the only capacity for which the core of the full Bayesian updates of a capacity, introduced by Jaffray, equals the set of Bayesian updates of the probability distributions in the core of the original capacity.