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Conditionally Additive Utility Representations

Qin, Wei-zhi and Rommeswinkel, Hendrik (2017): Conditionally Additive Utility Representations.

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Abstract

Advances in behavioral economics have made decision theoretic models increasingly complex. Utility models incorporating insights from psychology often lack additive separability, a major obstacle for decision theoretic axiomatizations. We address this challenge by providing a representation theorem for utility functions of the form $u(x,y,z)=f(x,z) + g(y,z)$. We call these representations conditionally additive as they are additively separable only when holding fixed $z$. We generalize the result to spaces with more than three dimensions. We provide axiomatizations for consumption preferences with reference points, as well as consumption preferences over time with dependence across time periods. Our results also allow us to generalize the theory of additive representations to simplexes.

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