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Almost Quasi-linear Utilities in Disguise: Positive-representation An Extension of Roberts' Theorem [article]

Ilan Nehama
2019 arXiv   pre-print
In this work, we generalize these results and define a new class of preferences: Preferences which are positive-represented by a quasi-linear utility.  ...  That is, agents whose preference on a subspace of the outcomes can be modeled using a quasi-linear utility.  ...  We note that the quasi-linear representations of a preference are closed to shifts by a constant and in particular a preference can be represented by a continuum of quasi-linear utility functions.  ... 
arXiv:1910.12131v1 fatcat:qivj4ogb4zat3ip5ffxrx77uyu

Preferences over all random variables: Incompatibility of convexity and continuity

Hirbod Assa, Alexander Zimper
2018 Journal of Mathematical Economics  
As an implication of this incompatibility result there cannot exist any non-trivial continuous utility representations over all random variables that are either quasiconcave or quasi-convex.  ...  This rules out standard risk-averse (or seeking) utility representations for this large space of random variables.  ...  For the EU representation (25) quasi-concavity (resp. quasi-convexity) of U is simply implied by concavity (resp. convexity) of u.  ... 
doi:10.1016/j.jmateco.2017.12.006 fatcat:nvaw5rixnzcy3ki3ponym3jo5m

Quasi equilibria for growth economies

Jonathan L. Burke
2009 Economics Letters  
Such economies have no competitive equilibria, but have quasi equilibria. And the supporting price systems include a type of speculative bubble. J.E.L. Classification Numbers: C6, E3.  ...  We find preferences that discount utility from future consumption yet violate the standard growth condition in representative-agent endowment economies.  ...  Standard representation and continuity properties of preferences depend on δ: (3) is not representable by any utility function, and in any linear topology on the commodity space the order is neither  ... 
doi:10.1016/j.econlet.2009.07.005 fatcat:uecn3ztflbh3lc5b6burrnqr2a

A class of convex preferences without concave representation

Paulo Klinger Monteiro
2010 Revista Brasileira de Economia  
In other words a preference relation with affine indifference curves that has a concave representation has a linear utility representation.  ...  Em outras palavras, uma relação de preferências com curvas de indiferença afins que tem representação côncava tem na verdade uma representação linear. * I acknowledge the help of H.  ...  In other words, a preference relation with affine indifference curves that has a concave representation necessarily has a linear utility representation.  ... 
doi:10.1590/s0034-71402010000100006 fatcat:c4qdiw7emndmbgg4aqke53kdeq

"Making Book Against Oneself," The Independence Axiom, and Nonlinear Utility Theory

Jerry Green
1987 Quarterly Journal of Economics  
The independence condition is necessary for the representability of preferences by a linear functional over the space of all probability distributions.  ...  Letting W(L) = V{FL), W{-) serves as a numerical representation of this preference.  ... 
doi:10.2307/1884281 fatcat:zm7qsuloqbdcdomloxozvl5k3i

Revealed cardinal preference

József Sákovics
2013 Economic Theory Bulletin  
I prove that as long as we allow the marginal utility for money (λ) to vary between purchases (similarly to the budget), then the quasi-linear and the ordinal budget-constrained models rationalize the  ...  I provide a simple constructive proof for the necessary and sufficient condition for the constant λ rationalization, which I argue should replace the Generalized Axiom of Revealed Preference in empirical  ...  is replaced by a quasi-linear utility function.  ... 
doi:10.1007/s40505-013-0006-4 fatcat:7nwzjiqpl5avbhaec7l5hxg33m

Determination of Break-Even Point through Consumer Preference Relation

Gopal Man Pradhan, Phanindra Kumar Katel
2021 The Batuk  
Preference relation with affine indifference curves that has a concave representation has a linear utility representation.  ...  This study asks how individual preference relations might be combined to give a single ordering which captures the overall wishes of the group of individuals.  ...  The strict preference is defined by x y x y and y not successor and equal x. The preference relation is a linear order if it is a complete partial order.  ... 
doi:10.3126/batuk.v7i2.39503 fatcat:hoz62krkdnaq3dhfibx67juwmy

Invariant risk attitudes

John Quiggin, Robert G Chambers
2004 Journal of Economic Theory  
The properties of the capital asset pricing model, usually expressed in terms of the mean and standard deviation, may be extended to the case of general invariant preferences. r  ...  Invariant risk aversion is closely related to the possibility of representing preferences over state-contingent income vectors in terms of two parameters, the mean and a linearly homogeneous, translation-invariant  ...  Acknowledgments We thank Simon Grant, Tigran Melkonyan, and an anonymous referee for helpful comments on earlier versions of this paper. All errors, of course, are our own.  ... 
doi:10.1016/j.jet.2003.09.006 fatcat:3y6epgqfi5g2xauxclfq3xt7ui

Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions [article]

William B. Haskell, Wenjie Huang, Huifu Xu
2018 arXiv   pre-print
Decision maker's preferences are often captured by some choice functions which are used to rank prospects.  ...  We propose two approaches based respectively on the support functions and level functions of quasi-concave functions to develop tractable formulations of the maximin preference robust optimization model  ...  This research is supported by MOE Tier II grant MOE2014-T2-1-066 and MOE Tier I grant WBS R-266-000-083-133.  ... 
arXiv:1805.06632v1 fatcat:k6fagzxuknff7nvqgmotsarz44

Page 3470 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
The main result is the existence of minimal representations of semiorders which can be calculated by linear programming and interpreted as a generalisation of the rank function associated to linear orders  ...  This neutrality axiom is similar to axioms used in social choice theory and means intuitively that preference is invariant under injective mappings and does not depend on the “labelling” of the alternatives  ... 

A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting

Nina Anchugina
2016 Theory and Decision  
The papers by Hayashi (2003) and Olea and Strzalecki (2014) axiomatize quasi-hyperbolic discounting.  ...  The main goal of this paper is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting.  ...  A quasi-hyperbolic representation of preferences can be obtained along similar lines to an exponential discounting representation with only minor modications of the axioms.  ... 
doi:10.1007/s11238-016-9566-8 fatcat:gbh4z6kv5fd63addb2solv4fv4

Notes on supermodularity and increasing differences in expected utility

Alejandro Francetich
2013 Economics Letters  
These notes provide axiomatic foundations for these properties on expectedutility representations of preferences over lotteries. an anonymous referee, for helpful comments and suggestions to improve these  ...  Many choice-theoretic and game-theoretic applications in Economics invoke some form of supermodularity or increasing differences for objective functions defined on lattices.  ...  Introduction These notes revisit the axiomatic foundations of the properties of supermodularity and of increasing differences for expected-utility representations of preferences defined over lotteries.  ... 
doi:10.1016/j.econlet.2013.08.009 fatcat:wqfswko4nbhdndzswmgjniaema

Mean-Dispersion Preferences and Constant Absolute Uncertainty Aversion

Simon Harold Grant, Ben Polak
2011 Social Science Research Network  
We axiomatize, in an Anscombe-Aumann framework, the class of preferences that admit a representation of the form V (f ) = (d), where is the mean utility of the act f with respect to a given probability  ...  , d is the vector of state-by-state utility deviations from the mean, and (d) is a measure of (aversion to) dispersion that corresponds to an uncertainty premium.  ...  This dispersion function is comonotonically linear (hence linear homogenous). Thus, by corollary 3, part (f), the corresponding mean-dispersion preferences are CEU.  ... 
doi:10.2139/ssrn.1861353 fatcat:jh4mecovxvb3zi75skyscyhwnq

Mean-dispersion preferences and constant absolute uncertainty aversion

Simon Grant, Ben Polak
2013 Journal of Economic Theory  
We axiomatize, in an Anscombe-Aumann framework, the class of preferences that admit a representation of the form V (f ) = (d), where is the mean utility of the act f with respect to a given probability  ...  , d is the vector of state-by-state utility deviations from the mean, and (d) is a measure of (aversion to) dispersion that corresponds to an uncertainty premium.  ...  This dispersion function is comonotonically linear (hence linear homogenous). Thus, by corollary 3, part (f), the corresponding mean-dispersion preferences are CEU.  ... 
doi:10.1016/j.jet.2012.11.003 fatcat:b3sem2rf6bfzpdsbsxzpuawqga

ON THE IMPLEMENTATION OF PREFERENCE RELATIONAL SYSTEMS IN A COMPUTER-AIDED DECISION SUPPORT SYSTEM

JOSÉ A. MORENO
1994 Cybernetics and systems  
the mixed transitivities), by the properties of the functions in the value-threshold support, by the circuits in the graph representation and by the shapes of the matrix representation.  ...  These structures (the preorder, the semiorder, the interval order, the quasi-order, the double semiorder and the pseudo-order) are characterized by essential implications (the simplest consequences of  ...  the mixed transitivities), by the properties of the functions in the value-threshold support, by the circuits in the graph representation and by the shapes of the matrix representation.  ... 
doi:10.1080/01969729408902313 fatcat:5ibj56k7bnflhdlumqoiapifza
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