Qin, Weizhi and Rommeswinkel, Hendrik (2017): Conditionally Additive Utility Representations.
This is the latest version of this item.
Preview 
PDF
MPRA_paper_80912.pdf Download (475kB)  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 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.
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:  80912 
Depositing User:  Prof. Hendrik Rommeswinkel 
Date Deposited:  21 Aug 2017 22:15 
Last Modified:  27 Sep 2019 05:36 
References:  Abdellaoui, M. (2009). RankDependent Utility. In Anand, P., Pattanaik, P. K., and Puppe, C., editors, The Handbook of Rational and Social Choice, pages 6989. Oxford University Press, Oxford, UK. Chew, S. H. and Sagi, J. S. (2008). Small worlds: Modeling attitudes toward sources of uncertainty. Journal of Economic Theory, 139(1):124. Debreu, G. (1959). Topological Methods in Cardinal Utility Theory. In Arrow, K. J., Karlin, P., and Suppes, P., editors, Mathematial Methods in the Social Sciences, pages 1626. Stanford University Press, Stanford. Dreze, J. H. and Rustichini, A. (1999). Moral hazard and conditional prefer ences. Journal of Mathematical Economics, 31(2):159181. Fehr, E. and Schmidt, K. M. (1999). A theory of fairness, competition, and cooperation. The quarterly journal of economics, 114(3):817868. Gorman, W. M. (1968). The Structure of Utility Functions. The Review of Economic Studies, 35(4):367390. Herstein, I. N. and Milnor, J. (1953). An Axiomatic Approach to Measurable Utility. Econometrica, 21(2):291297. Hosszu, M. (1971). On the functional equation F(x+y,z)+F(x,y)=F(x,y+z)+F(y,z). Periodica Mathematica Hungarica, 1:213216. Karni, E. (1998). The Hexagon Condition and Additive Representation for Two Dimensions: An Algebraic Approach. Journal of Mathematical Psychology, 42:393399. Karni, E. (2006). Subjective expected utility theory without states of the world. Journal of Mathematical Economics, 42(3):325342. Kydland, F. E. and Prescott, E. C. (1982). Time to Build and Aggregate Fluctuations. Econometrica, 50(6):13451370. Munkres, J. (2014). Topology. Pearson, Essex, UK. Neilson, W. S. (2006). Axiomatic referencedependence in behavior toward others and toward risk. Economic Theory, 28(3):681692. Puppe, C. (1990). The irrelevance axiom, relative utility and choice under risk. Quiggin, J. (1982). A Theory of Anticipated Utility. Journal of Economic Behavior and Organization, 3:323343. Reidemeister, K. (1929). Topologische Fragen der Differentialgeometrie. V. Gewebe und Gruppen. Mathematische Zeitschrift, 29(1):427435. Rohde, K. I. M. (2010). A preference foundation for Fehr and Schmidt's model of inequity aversion. Social Choice and Welfare, 34(4):537547. Rozen, K. (2010). Foundations of Intrinsic Habit Formation. Econometrica, 78(4):13411373. Ryder, H. E. and Heal, G. M. (1973). Optimal Growth with Intertemporally Dependent Preferences. The Review of Economic Studies, 40(1):131. Savage, L. J. (1972). The Foundations of Statistics. Courier Corporation. Segal, U. (1989). Anticipated utility: A measure representation approach. Annals of Operations Research, 19(1):359373. Segal, U. (1992). Additively Separable Representation on Nonconvex Sets. Journal of Economic Theory, 56:8999. Segal, U. (1993). The measure representation: A correction. Journal of Risk and Uncertainty, 6(1):99107. Sugden, R. (2003). Referencedependent subjective expected utility. Journal of Economic Theory, 111(2):172191. Tversky, A. and Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and uncertainty, 5(4):297323. Vind, K. (1991). Independent preferences. Journal of Mathematical Economics, 20(1):119135. von Neumann, J. and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press. Wakai, K. (2007). Risk NonSeparability without Force of Habit. Wakker, P. (1993). Counterexamples to Segal's measure representation theorem. Journal of Risk and Uncertainty, 6(1):9198. Wakker, P. and Chateauneuf, A. (1993). From local to global additive representation. Journal of Mathematical Economics, 22:523545. Wakker, P. and Tversky, A. (1993). An axiomatization of cumulative prospect theory. Journal of risk and uncertainty, 7(2):147175. Wakker, P. P. (1989). Additive Representations of Preferences: A New Foundation of Decision Analysis, volume 4. Springer Science & Business Media. Wang, T. (2003). Conditional preferences and updating. Journal of Economic Theory, 108(2):286321. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/80912 
Available Versions of this Item

Conditionally Additive Utility Representations. (deposited 06 Apr 2017 13:51)
 Conditionally Additive Utility Representations. (deposited 21 Aug 2017 22:15) [Currently Displayed]