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Symmetry
Special Issues
Game-Theoretical Symmetry under Dynamic Processes
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Game-Theoretical Symmetry under Dynamic Processes

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 May 2022) | Viewed by 6127

Special Issue Editors

Dr. Yu-Hsien Liao

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Guest Editor
Department of Applied Mathematics, National Pingtung University, Pingtung 900, Taiwan
Interests: game theory
Prof. Dr. Yan-An Hwang

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Guest Editor
Department of Applied Mathematics, National Dong Hwa University, Taiwan
Interests: game theory; mathematical economics
Prof. Dr. Wei-Shih Du

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Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis; fixed point theory and its applications; variational principles and inequalities; optimization theory; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Hui-Chuan Wei

E-Mail Website
Guest Editor
Department of Adult and Continuing Education, National Chung-Cheng University, Taiwan
Interests: designing and planning learning programs and projects for middle aged and above; social choice and welfare; management sciences

Special Issue Information

Dear Colleagues,

Symmetry exists in many different phenomena or academic fields, which of course also includes game theory. In game theory, the construction and analysis of “solutions” is an extremely important issue. Axiomatic processes are often applied to the construction of solutions and the analysis of their related properties, while dynamic processes are to discuss how general results approach a state of equilibrium through specific processes. In the above two types of processes, the relative symmetry between the process and the related results is often discussed. Therefore, the main purpose of this Special Issue is to explore the relative symmetry of all forms under axiomatic processes and dynamic processes in game theory.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Game-Theoretical Symmetry under Dynamic Processes” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Dr. Yu-Hsien Liao
Prof. Dr. Yan-An Hwang
Prof. Dr. Wei-Shih Du
Prof. Dr. Hui-Chuan Wei
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • game theory
  • solution
  • axiomatic processes
  • dynamic processes
  • equilibrium

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Published Papers (3 papers)

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Research

8 pages, 581 KiB  
Article
Optimal Number of Pursuers in Differential Games on the 1-Skeleton of an Orthoplex
by Abdulla Azamov, Gafurjan Ibragimov, Tolanbay Ibaydullaev and Idham Arif Alias
Symmetry 2021, 13(11), 2170; https://doi.org/10.3390/sym13112170 - 12 Nov 2021
Cited by 4 | Viewed by 1884
Abstract
We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the [...] Read more.
We study a differential game of many pursuers and one evader. All the players move only along the one-skeleton graph of an orthoplex of dimension d+1. It is assumed that the maximal speeds of the pursuers are less than the speed of the evader. By definition, the pursuit is completed if the position of a pursuer coincides with the position of the evader. Evasion is said to be possible in the game if the movements of players are started from some initial positions and the position of the evader never coincides with the position of any pursuer. We found the optimal number of pursuers in the game. The symmetry of the orthoplex plays an important role in the construction of the players’ strategies. Full article
(This article belongs to the Special Issue Game-Theoretical Symmetry under Dynamic Processes)
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10 pages, 265 KiB  
Article
Game-Theoretic Dynamic Procedure for a Power Index under Relative Symmetry
by Jong-Chin Huang, Kelvin H.-C. Chen and Yu-Hsien Liao
Symmetry 2021, 13(10), 1921; https://doi.org/10.3390/sym13101921 - 13 Oct 2021
Cited by 1 | Viewed by 1233
Abstract
In many operational processes, a suitable combination of participating elements has a huge impact throughout the entire process. In the real environment, however, many combinations show less than expected results in the initial stage. In consideration of the many subjective and objective factors [...] Read more.
In many operational processes, a suitable combination of participating elements has a huge impact throughout the entire process. In the real environment, however, many combinations show less than expected results in the initial stage. In consideration of the many subjective and objective factors such as equipment, time, capital, materials, and so forth, it seems that the aforementioned combinations cannot be used to re-configure. It is important that these initial unsatisfactory combinations can gradually approach some equilibrium states or results through some rolling adjustment processes. In order to improve the above problem, this study attempts to use a game-theoretic dynamic procedure to establish a mechanism that can be dynamically modified under relative symmetry at any time during operational processes. Under such a dynamic procedure, an undesirable combination of participating elements can gradually approach a useful combination. Full article
(This article belongs to the Special Issue Game-Theoretical Symmetry under Dynamic Processes)
12 pages, 259 KiB  
Article
Axiomatic and Dynamic Processes for a Symmetric Allocation Rule
by Chia-Hung Li, Jo-Wei Chiang, En-Cheng Chi and Yu-Hsien Liao
Symmetry 2021, 13(8), 1474; https://doi.org/10.3390/sym13081474 - 11 Aug 2021
Cited by 2 | Viewed by 1348
Abstract
It has recently become imperative to analyze relevant issues to improve the efficiency of resource allocation by means of different perspectives and ways of thinking. There exist numerous decisive factors, such as changes in forms of allocation, reactive behavior, and the interaction and [...] Read more.
It has recently become imperative to analyze relevant issues to improve the efficiency of resource allocation by means of different perspectives and ways of thinking. There exist numerous decisive factors, such as changes in forms of allocation, reactive behavior, and the interaction and functional effectiveness of strategies, that need to be complied. In contrast to expert meetings, rules of thumb, or other existing concepts, this article aims to offer a different and efficient resource allocation approach by applying game-theoretical methods to resource-allocation situations. Our major investigative procedures are as follows: (1) after comparing our method with pre-existing allocation rules from pre-existing allocation rules, a symmetric allocation rule is proposed that considers both units and their energy grades; (2) based on the properties of grade completeness, criterion for models, unmixed equality symmetry, grade synchronization, and consistency, some axiomatic outcomes are used to examine the mathematical accuracy and the applied rationality of this symmetric allocation rule; (3) based on a symmetrical revising function, a dynamic process is applied to show that this symmetric allocation rule can be reached by units that start from an arbitrary grade completeness situation; and (4) these axiomatic and dynamic results and related meanings are applied to show that this symmetric allocation rule can present an optimal alternative guide for resource-allocation processes. Related applications, comparisons, and statements are also offered throughout this article. Full article
(This article belongs to the Special Issue Game-Theoretical Symmetry under Dynamic Processes)
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