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A Themed Issue Dedicated to Professor Lloyd S. Shapley on...
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A Themed Issue Dedicated to Professor Lloyd S. Shapley on the Occasion of His 100th Birthday Anniversary

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

Deadline for manuscript submissions: closed (2 June 2023) | Viewed by 2383

Special Issue Editors

Dr. Burak Erkut

E-Mail Website
Guest Editor
Department of Business, Faculty of Business and Economics, Eastern Mediterranean University, Gazimağusa 99628, Turkey
Interests: evolutionary economics; innovation; entrepreneurship
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Fatih Ecer

E-Mail Website
Guest Editor
Faculty of Economics and Administrative Sciences, Afyon Kocatepe University, Afyonkarahisar, Turkey
Interests: decision science; optimization; MCDM; fuzzy sets

Special Issue Information

Dear Colleagues,

We are pleased to introduce this Special Issue dedicated to Professor Lloyd S. Shapley on the occasion of his 100th Birthday Anniversary. Professor Lloyd S. Shapley was considered a leading scholar who contributed to the establishment and growth of the mathematical discipline of game theory. In his research, Professor Lloyd S. Shapley considered both cooperative and non-cooperative game theoretical concepts and contributed to our understanding of stochastic games, strategic market games, assignment games, cooperative and non-cooperative market models, voting games and power indices, potential games, and cost allocation and organization theory. Specifically, we know him from his work on the “Shapley value” and the “core”. In this instance, this Special Issue will focus on state-of-the-art research on non-cooperative and cooperative game theory both to memorize Professor Shapley and to contribute to the agenda of game theory and its applications in the ongoing research scene.

Dr. Burak Erkut
Prof. Dr. Fatih Ecer
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 game theory
  • non-cooperative game theory
  • Shapley value

Published Papers (2 papers)

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Research

14 pages, 306 KiB  
Article
Shapley Mapping and Its Axiomatizations in n-Person Cooperative Interval Games
by Junnosuke Shino, Shinichi Ishihara and Shimpei Yamauchi
Mathematics 2022, 10(21), 3963; https://doi.org/10.3390/math10213963 - 25 Oct 2022
Cited by 2 | Viewed by 1178
Abstract
Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval, instead of a real number. In this paper, we first examine the notion of solution mapping, a solution [...] Read more.
Interval games are an extension of cooperative coalitional games, in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval, instead of a real number. In this paper, we first examine the notion of solution mapping, a solution concept applied to interval games, by comparing it with the existing solution concept called the interval solution concept. Then, we define a Shapley mapping as a specific form of the solution mapping. Finally, it is shown that the Shapley mapping can be characterized by two different axiomatizations, both of which employ interval game versions of standard axioms used in the traditional cooperative game analysis such as efficiency, symmetry, null player property, additivity and separability. Full article
(This article belongs to the Special Issue A Themed Issue Dedicated to Professor Lloyd S. Shapley on the Occasion of His 100th Birthday Anniversary)
10 pages, 259 KiB  
Article
On Balanced Host Games: A Sufficient Condition for Non-Emptiness of the Core
by Yan-An Hwang, Yu-Hsien Liao and Bo-Yao Wang
Mathematics 2022, 10(20), 3897; https://doi.org/10.3390/math10203897 - 20 Oct 2022
Viewed by 778
Abstract
Non-transferable utility (NTU) games arise from many economic situations. A classic example is the exchange economy. By pooling and redistributing their initial endowments, coalitions can achieve certain distributions of gains (utilities) that make up the coalition’s feasible set. This paper studies a new [...] Read more.
Non-transferable utility (NTU) games arise from many economic situations. A classic example is the exchange economy. By pooling and redistributing their initial endowments, coalitions can achieve certain distributions of gains (utilities) that make up the coalition’s feasible set. This paper studies a new class of NTU games called host games. A host game is an agent-parametrized family of NTU games, and an NTU game is associated with any agent (called the host in that case). We provide an adequate presumption for the existence of an allocation that is part of the host game’s core. Full article
(This article belongs to the Special Issue A Themed Issue Dedicated to Professor Lloyd S. Shapley on the Occasion of His 100th Birthday Anniversary)
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