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Mathematics
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Mathematical Economics and Its Applications
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Mathematical Economics and Its Applications

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 30 November 2024 | Viewed by 2898

Special Issue Editor

Prof. Dr. Alfio Giarlotta

E-Mail Website
Guest Editor
Department of Economics and Business, University of Catania, 95131 Catania, Italy
Interests: preference modeling; choice theory; bounded rationality; multiple criteria decision analysis; mathematical utility theory; general topology; set theory; combinatorics; logic

Special Issue Information

Dear Colleagues,

Research in several fields of mathematical economics has been growing quite fast in the last 20 years, due also to potential applications in real-world scenarios.

The mathematical tools employed in this research come from a wide spectrum of areas, e.g., algebra, analysis, measure theory, probability theory, combinatorics, topology, set theory, and mathematical logic.

This Special Issue aims to collect recent results in several areas of interest in mathematical economics.

We invite papers presenting original research on related topics, including, but not limited to, the following:

  • Preference modeling;
  • Order theory;
  • Choice theory;
  • Bounded rationality;
  • Decision theory;
  • Mathematical utility theory.

Prof. Dr. Alfio Giarlotta
Guest Editor

Mr. Davide Carpentiere
Guest Editor Assistant
Affiliation: Department of Mathematics and Computer Science, University of Catania, Catania, Italy
E-mail:
Interests: preference modeling; choice theory; set theory; general topology; algebraic topology; combinatorics; commutative algebra; category theory

Mr. Angelo Petralia
Guest Editor Assistant
Affiliation: Department of Economics, Collegio Carlo Alberto, Torino, Italy
E-mail:
Interests: microeconomic theory; bounded rationality; choice theory; decision theory

Ms. Ester Sudano
Guest Editor Assistant
Affiliation: School of Economics and Finance, Queen Mary University of London, London, UK
E-mail:
Interests: microeconomic theory; bounded rationality; individual and social choice; stochastic choice

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • preference modeling
  • semiorder and interval order
  • individual choice theory
  • social choice theory
  • bounded rationality
  • decision theory
  • mathematical utility theory

Published Papers (4 papers)

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Research

9 pages, 292 KiB  
Article
Properties of Topologies for the Continuous Representability of All Weakly Continuous Preorders
by Gianni Bosi, Laura Franzoi and Gabriele Sbaiz
Mathematics 2023, 11(20), 4335; https://doi.org/10.3390/math11204335 - 18 Oct 2023
Viewed by 639
Abstract
We investigate properties of strongly useful topologies, i.e., topologies with respect to which every weakly continuous preorder admits a continuous order-preserving function. In particular, we prove that a topology is strongly useful provided that the topology generated by every family of separable [...] Read more.
We investigate properties of strongly useful topologies, i.e., topologies with respect to which every weakly continuous preorder admits a continuous order-preserving function. In particular, we prove that a topology is strongly useful provided that the topology generated by every family of separable systems is countable. Focusing on normal Hausdorff topologies, whose consideration is fully justified and not restrictive at all, we show that strongly useful topologies are hereditarily separable on closed sets, and we identify a simple condition under which the Lindelöf property holds. Full article
(This article belongs to the Special Issue Mathematical Economics and Its Applications)
19 pages, 369 KiB  
Article
Undominated Maximals: General Definition and Characterizations
by Federico Quartieri
Mathematics 2023, 11(18), 3879; https://doi.org/10.3390/math11183879 - 11 Sep 2023
Viewed by 428
Abstract
This paper proposes a general definition of an undominated maximal of a relation on a constraint set. No specific requirement is imposed on either the asymmetry of the objective relation or the constraint set (which might, or might not, coincide with the ground [...] Read more.
This paper proposes a general definition of an undominated maximal of a relation on a constraint set. No specific requirement is imposed on either the asymmetry of the objective relation or the constraint set (which might, or might not, coincide with the ground set of the objective relation). Several characterizations are formulated that express undominated maximals of an objective relation as maximals of some trace associated with that objective relation. By means of some of these characterizations, the structure of the entire set of undominated maximals is examined in the particular case of relations induced by open and closed convex cones—among them, the weak and strong Pareto dominance—and, in the case of semiorders, that admit certain types of representability. The results of the last part of the examination allow the construction of many examples of relations whose entire sets of maximals and undominated maximals are completely identifiable in an elementary way. Full article
(This article belongs to the Special Issue Mathematical Economics and Its Applications)
10 pages, 286 KiB  
Article
Rights Systems and Aggregation Functions on Property Spaces
by Marta Cardin
Mathematics 2023, 11(17), 3709; https://doi.org/10.3390/math11173709 - 29 Aug 2023
Viewed by 503
Abstract
The notion of decisive coalitions of voters with different grades of decisiveness is a part of the mathematical framework for many models in social choice theory. More generally, we study aggregation problems in which a subgroup of decision makers have the right to [...] Read more.
The notion of decisive coalitions of voters with different grades of decisiveness is a part of the mathematical framework for many models in social choice theory. More generally, we study aggregation problems in which a subgroup of decision makers have the right to determine the properties of the aggregate. Then, we introduce property spaces and rights to properties and characterize aggregation operators that are consistent with rights to properties. Moreover, we define congruences in property spaces, and we propose a generalization of the Sugeno integral in our framework. Full article
(This article belongs to the Special Issue Mathematical Economics and Its Applications)
19 pages, 353 KiB  
Article
Quasi-Metrics for Possibility Results: Intergenerational Preferences and Continuity
by Asier Estevan, Roberto Maura and Óscar Valero
Mathematics 2023, 11(2), 395; https://doi.org/10.3390/math11020395 - 12 Jan 2023
Viewed by 756
Abstract
In this paper, we provide the counterparts of a few celebrated impossibility theorems for continuous social intergenerational preferences according to P. Diamond, L.G. Svensson and T. Sakai. In particular, we give a topology that must be refined for continuous preferences to satisfy anonymity [...] Read more.
In this paper, we provide the counterparts of a few celebrated impossibility theorems for continuous social intergenerational preferences according to P. Diamond, L.G. Svensson and T. Sakai. In particular, we give a topology that must be refined for continuous preferences to satisfy anonymity and strong monotonicity. Furthermore, we suggest quasi-pseudo-metrics as an appropriate quantitative tool for reconciling topology and social intergenerational preferences. Thus, we develop a metric-type method which is able to guarantee the possibility counterparts of the aforesaid impossibility theorems and, in addition, it is able to give numerical quantifications of the improvement of welfare. Finally, a refinement of the previous method is presented in such a way that metrics are involved. Full article
(This article belongs to the Special Issue Mathematical Economics and Its Applications)
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