Qin, Weizhi and Rommeswinkel, Hendrik (2017): Conditionally Additive Utility Representations.
There is a more recent version of this item available. 

PDF
MPRA_paper_78158.pdf Download (373kB)  Preview 
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 representation theorems which yield utility functions of the form u(x,y,z)=f(x,z) + g(y,z). We call these representations conditionally separable as they are additively separable only once holding fixed z. Our representation theorems have a wide range of applications. For example, extensions to finitely many dimensions yield both consumption preferences with reference points Sum_i u_i(x_i,r), as well as consumption preferences over time with dependence across time periods Sum_t u_t(x_t,x_{t1}).
Item Type:  MPRA Paper 

Original Title:  Conditionally Additive Utility Representations 
Language:  English 
Keywords:  utility; representation theorem; additive; conditionally additive; ordered space 
Subjects:  D  Microeconomics > D0  General > D01  Microeconomic Behavior: Underlying Principles D  Microeconomics > D0  General > D03  Behavioral Microeconomics: Underlying Principles D  Microeconomics > D1  Household Behavior and Family Economics > D11  Consumer Economics: Theory 
Item ID:  78158 
Depositing User:  Prof. Hendrik Rommeswinkel 
Date Deposited:  06 Apr 2017 13:51 
Last Modified:  27 Sep 2019 16:05 
References:  Aliprantis, C. D. and Border, K. C. (2006). Infinite Dimensional Analysis, Springer, 3 edition. Debreu, G. (1954). Representation of a preference ordering by a numerical function. Decision processes, 3:159165. Herstein, I. N. and Milnor, J. (1953). An Axiomatic Approach to Measurable Utility. Econometrica, 21(2):291. Kahneman, D. and Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the econometric society, pages 263291. M.Hosszu (1971). On the functional equation F(x+y,z)+F(x,y)=F(x,y+z)+F(y,z). Periodica Mathematica Hungarica, 1:213216. Rozen, K. (2010). Foundations of Intrinsic Habit Formation. Econometrica, 78(4):13411373. Sugden, R. (2003). Referencedependent subjective expected utility. Journal of Economic Theory, 111(2):172191. Vind, K. (1991). Independent preferences. Journal of Mathematical Economics, 20(1):119135. Wakker, P. and Chateauneuf, A. (1993). From local to global additive representation. Journal of Mathematical Economics, 22:523545. Wakker, P. P. (1989). Additive Representations of Preferences: A New Foundation of Decision Analysis, volume 4. Springer Science & Business Media. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/78158 
Available Versions of this Item
 Conditionally Additive Utility Representations. (deposited 06 Apr 2017 13:51) [Currently Displayed]