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Mathematics
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Trends in Game Theory and Its Applications
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Trends in Game Theory and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 5585

Special Issue Editors

Prof. Dr. Encarnación Algaba

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Guest Editor
Department of Applied Mathematics II and IMUS, University of Seville, 41092 Sevilla, Spain
Interests: analysis of networks; cooperative game theory; restricted cooperation
Dr. Stefano Moretti

E-Mail Website
Guest Editor
LAMSADE, CNRS, Paris-Dauphine University, Université PSL, 75016 Paris, France
Interests: axiomatic analysis of solutions for cooperative games and their applications; design of efficient algorithms in strategic games arising from combinatorial problems; power indices and related social choice problems; bioinformatics and statistical analysis of biological data of human RNA
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Marina Núñez

E-Mail Website
Guest Editor
Department of Economic, Financial and Actuarial Mathematics, University of Barcelona, Av. Diagonal, 690, Barcelona, Spain
Interests: game theory; mathematical economics; matching; mechanism design
Prof. Dr. Agnieszka Rusinowska

E-Mail Website
Guest Editor
CNRS, Centre d'Economie de la Sorbonne, Maison des Sciences Economiques, 106-112 Boulevard de l'Hôpital, 75647 Paris Cedex 13, France
Interests: microeconomic theory; game theory; operations research; social choice theory: social and economic networks, influence, coalitions, alliances, voting power, bargaining theory

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to the European Meeting on Game Theory—SING16. These scientific meetings have a long tradition in Europe, and their origins date back to the early 1980s. It can now be said that the European Meetings on Game Theory, better known as SING Meetings, are the main congress on game theory held in Europe, bringing researchers from all over the world together. It is a forum where new results, advances and trends in game theory are presented and disseminated.

We would like to invite participants in SING16 to consider this Special Issue to submit their original papers—both those presented during the congress and other relevant papers. Of course, we also invite any other game theorists who have not participated in SING16 to submit their original papers to this Special Issue.

Therefore, the main aim of this Special Issue in Mathematics is to gather a collection of papers that reflect the latest results, advances and trends in game theory and its applications, particularly, but not limited to, those areas covered by the SING Meetings.

Prof. Dr. Encarnación Algaba
Prof. Dr. Stefano Moretti
Prof. Dr. Marina Núñez
Prof. Dr. Agnieszka Rusinowska
Guest Editors

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

  • Cooperative games and their applications
  • Voting
  • Power indices
  • Cost sharing and resource allocation
  • Mechanism design
  • Dynamic games
  • Noncooperative games
  • Networks
  • Matching
  • Learning and experimentation in games
  • Social choice
  • Auctions
  • Computational game theory

Published Papers (4 papers)

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Research

22 pages, 517 KiB  
Article
Social Ranking Problems at the Interplay between Social Choice Theory and Coalitional Games
by Felix Fritz, Stefano Moretti and Jochen Staudacher
Mathematics 2023, 11(24), 4905; https://0-doi-org.brum.beds.ac.uk/10.3390/math11244905 - 08 Dec 2023
Viewed by 622
Abstract
This paper reviews the recent literature on the “social ranking problem”, that is, the problem of converting group rankings into individual rankings. We introduce and categorize existing social ranking methods and we briefly explain their attributes. Three main categories of social ranking methods [...] Read more.
This paper reviews the recent literature on the “social ranking problem”, that is, the problem of converting group rankings into individual rankings. We introduce and categorize existing social ranking methods and we briefly explain their attributes. Three main categories of social ranking methods are identified: lexicographic social rankings, methods based on voting mechanisms, and those inspired by the theory of coalitional games. An open-source R package called socialranking for computing the majority of the existing social rankings is also presented and discussed. Full article
(This article belongs to the Special Issue Trends in Game Theory and Its Applications)
16 pages, 324 KiB  
Article
Properties of Solutions for Games on Union-Closed Systems
by Rene van den Brink, Ilya Katsev and Gerard van der Laan
Mathematics 2023, 11(4), 980; https://0-doi-org.brum.beds.ac.uk/10.3390/math11040980 - 14 Feb 2023
Viewed by 976
Abstract
A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions to every TU-game. In [...] Read more.
A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions to every TU-game. In the literature, various models of games with restricted cooperation can be found where, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper, we consider games on a union-closed system where the set of feasible coalitions is closed under the union, i.e., for any two feasible coalitions also, their union is feasible. Properties of solutions (the core, the nucleolus, and the prekernel) are discussed for games on a union-closed system. Full article
(This article belongs to the Special Issue Trends in Game Theory and Its Applications)
14 pages, 345 KiB  
Article
An Aggregation Rule Based on the Binomial Distribution
by Josep Freixas
Mathematics 2022, 10(23), 4418; https://0-doi-org.brum.beds.ac.uk/10.3390/math10234418 - 23 Nov 2022
Viewed by 881
Abstract
Many decision-making situations require the evaluation of several voters or agents. In a situation where voters evaluate candidates, the question arises of how best to aggregate evaluations so as to compare the candidates. The aim of this work is to propose a method [...] Read more.
Many decision-making situations require the evaluation of several voters or agents. In a situation where voters evaluate candidates, the question arises of how best to aggregate evaluations so as to compare the candidates. The aim of this work is to propose a method of aggregating the evaluations of the voters, which has outstanding properties and serve as a potential evaluative tool in many contexts. Ordered weighted averages is a family of rules appropriate for studying this problem. In this paper, I propose as a solution an ordered weighted average that satisfies compelling properties and whose weights are derived from the binomial distribution. Full article
(This article belongs to the Special Issue Trends in Game Theory and Its Applications)
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20 pages, 369 KiB  
Article
Cooperative Purchasing with General Discount: A Game Theoretical Approach
by Jose A. García-Martínez, Ana Meca and G. Alexander Vergara
Mathematics 2022, 10(22), 4195; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224195 - 09 Nov 2022
Cited by 1 | Viewed by 1282
Abstract
In some situations, sellers of certain commodities usually provide price discounts for large orders according to a decreasing unit price function. Buyers of such commodities can cooperate and form purchasing groups to benefit from these price discounts. A natural way to allocate the [...] Read more.
In some situations, sellers of certain commodities usually provide price discounts for large orders according to a decreasing unit price function. Buyers of such commodities can cooperate and form purchasing groups to benefit from these price discounts. A natural way to allocate the corresponding cost reductions is the equal price rule. We analyze this situation as a cooperative game. We show that when the decreasing unit price function is linear, the equal price rule coincides with the Shapley value and the nucleolus of the cooperative game. However, some buyers may argue that the equal price rule is not acceptable because it favors those who buy just a few units of the product. This can be more problematic when the decreasing unit price function is nonlinear: In that case, the equal price rule loses some of its good properties and it no longer matches the Shapley value or the nucleolus. Unlike the linear case, in this nonlinear case, the Shapley value and nucleolus do not assign the same price to all agents, so there are different price rules. However, they have a computability problem, as both are very laborious to calculate for a large number of agents. To find a suitable alternative, we first study the properties that a different price rule should have in this situation. Second, we propose a family of different price rules that hold those properties and are easy to calculate for a large number of agents. This family of different price rules provides buyers (companies, institutions, consumers, etc.) with an easy-to-implement method which ensures stability in cooperative purchasing. Full article
(This article belongs to the Special Issue Trends in Game Theory and Its Applications)
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