An operational test for the existence of a consistent increasing quasi-concave value function

Soleimani-damaneh, Majid; Pourkarimi, Latif; Korhonen, Pekka; Wallenius, Jyrki

doi:10.1016/j.ejor.2020.06.049

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2022

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Cited by 2 publications

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“…It could be interesting to consider further properties of a utility function, besides continuity. This is the case, for example, of quasi-concavity (see, e.g., Soleimani-damaneh et al [19]). In addition, the general framework of the Con-joint Measurement Problem could be, so to say, incorporated (see, e.g., Bouyssou and Marchant [6,7]).…”

Section: Discussionmentioning

confidence: 98%

A Simple Characterization of Useful Topologies in Mathematical Utility Theory

Bosi

Zuanon

2022

Bull. Iran. Math. Soc.

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In this paper we present a simple axiomatization of useful topologies, i.e. topologies on an arbitrary set, with respect to which every continuous total preorder admits a continuous utility representation. We introduce the concept of weak open and closed countable chain condition (WOCCC) relative to a topology, and we then show that a useful topology always satisfies this condition. The most important result in the paper shows that a completely regular topology is useful if and only if it is separable and it satisfies WFOCCC (a stricter version of WOCCC). In this way, we generalize all the previous results concerning useful topologies. We finish the paper by presenting a simple axiomatization of useful topologies under the well known Souslin Hypothesis.

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Section: Discussionmentioning

confidence: 98%