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Mathematics
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Application of Game Theory
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Application of Game Theory

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

Deadline for manuscript submissions: closed (30 January 2024) | Viewed by 3282

Special Issue Editors

Dr. Alexander A. Tarasyev

E-Mail Website
Guest Editor
Department of Systems Analysis and Decision Making, Research Laboratory on Problems of University Development, Ural Federal University named after the first President of Russia B.N. Yeltsin, 620002 Yekaterinburg, Russia
Interests: dynamic modeling; labor market; economics of education; business intelligence
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Alexander M. Tarasyev

E-Mail Website
Guest Editor
Dynamic Systems Department, N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 620990 Yekaterinburg, Russia
Interests: optimal control; dynamic optimization; nonlinear systems; differential games; Hamilton–Jacobi equations; mathematical modeling

Special Issue Information

Dear Colleagues,

In the last few decades, the role of the applications of systems analysis, game theory, scientific computing, and the theory of information systems has been instantly increasing, especially for the solution of real-world economic problems and applications to financial mathematics.

This Special Issue will present recent research results in applications of systems analysis, game theory approaches, and the theory of information systems in the modeling of sustainable economic development.

Papers will focus on systems analysis, dynamic optimization, the optimal control of nonlinear systems, dynamic games, the application of systems analysis to the modeling of economic processes, models of behavioral economics, models of economic growth, information systems development, and the computational performance of new and original methods in all areas of economics and finance. We welcome papers on topics including, but not limited to, the following areas:

  • optimal control;
  • nonlinear dynamic systems;
  • dynamic optimization;
  • state estimation;
  • differential games;
  • generalized solutions of Hamilton–Jacobi equations;
  • optimization and operations research;
  • applied systems analysis;
  • mathematical modeling in social, economic, financial, and behavioral sciences;
  • econometrics and scientific computing as well as algorithms in economics and finance.

We also welcome papers exploring applications of the optimal control theory and dynamic games to real-world problems in economics and financial mathematics.

Dr. Alexander A. Tarasyev
Prof. Dr. Alexander M. Tarasyev
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

  • optimal control
  • nonlinear systems
  • dynamic optimization
  • stability and stabilization
  • state estimation
  • theory of Hamilton–Jacobi equations
  • dynamic games
  • systems analysis
  • applications of the optimal control theory and numerical methods
  • mathematical modeling in social, economic, financial, and behavioral sciences

Published Papers (3 papers)

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Research

25 pages, 3436 KiB  
Article
Research on Decision Analysis with CVaR for Supply Chain Finance Based on Blockchain Technology
by Shujian Ma, Jilong Cai, Gang Wang, Xiangxiang Ge, Ying Teng and Hua Jiang
Mathematics 2024, 12(3), 438; https://doi.org/10.3390/math12030438 - 30 Jan 2024
Viewed by 709
Abstract
The application of blockchain has become a trend in the development of supply chain finance. Aiming to bridge the gap in the existing literature, this paper investigates a supply chain finance system based on blockchain technology which contains a manufacturer, a retailer and [...] Read more.
The application of blockchain has become a trend in the development of supply chain finance. Aiming to bridge the gap in the existing literature, this paper investigates a supply chain finance system based on blockchain technology which contains a manufacturer, a retailer and a financial institution and incorporates blockchain costs into the model. Firstly, this paper establishes a supply chain finance model based on blockchain technology and it presents a comparison with the process employed under the traditional model. Secondly, this paper establishes the revenue mathematical model of supply chain finance based on blockchain technology. Thirdly, the optimal decisions of each participant under centralized and decentralized decision-making are proved and obtained, respectively, and the influencing factors of the optimal decisions are analyzed. Finally, the conclusions are verified via simulations. This study finds that, when blockchain is used, the benefits of each participant in the chain are increased. In addition, centralized decision-making, which is more optimal in the traditional model, is also enhanced under blockchain. This paper demonstrates the superiority of blockchain-enabled supply chain finance in terms of model and revenue. This provides some suggestions for companies in the supply chain with regard to solving the problem of financing difficulties. Full article
(This article belongs to the Special Issue Application of Game Theory)
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10 pages, 382 KiB  
Article
Optimisation of Cycling Trends in Hamiltonian Systems of Economic Growth Models
by Alexander Mikhailovich Tarasyev, Anastasia Alexandrovna Usova and Alexander Alexandrovich Tarasyev
Mathematics 2023, 11(11), 2452; https://doi.org/10.3390/math11112452 - 25 May 2023
Cited by 1 | Viewed by 721
Abstract
The paper analyses dynamical growth models predicting the cyclic development of investigated economic factors. The provided research deals with an optimal control problem based on the economic growth model with the production function of Cobb–Douglas type. Following the Pontryagin maximum principle, we derived [...] Read more.
The paper analyses dynamical growth models predicting the cyclic development of investigated economic factors. The provided research deals with an optimal control problem based on the economic growth model with the production function of Cobb–Douglas type. Following the Pontryagin maximum principle, we derived the Hamiltonian system and conducted its qualitative analysis, which reveals conditions for the cyclic behaviour of the optimal solutions around the isolate steady state. Numerical experiments visually illustrated the obtained results by demonstrating a phase portrait corresponding to a steady state of the focal type. Full article
(This article belongs to the Special Issue Application of Game Theory)
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13 pages, 340 KiB  
Article
The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon
by Tatyana Balas and Anna Tur
Mathematics 2023, 11(2), 462; https://doi.org/10.3390/math11020462 - 15 Jan 2023
Cited by 1 | Viewed by 1259
Abstract
A differential game with random duration is considered. The terminal time of the game is a random variable settled using a composite distribution function. Such a scenario occurs when the operating mode of the system changes over time at the appropriate switching points. [...] Read more.
A differential game with random duration is considered. The terminal time of the game is a random variable settled using a composite distribution function. Such a scenario occurs when the operating mode of the system changes over time at the appropriate switching points. On each interval between switchings, the distribution of the terminal time is characterized by its own distribution function. A method for solving such games using dynamic programming is proposed. An example of a non-renewable resource extraction model is given, where a solution of the problem of maximizing the total payoff in closed-loop strategies is found. An analytical view of the optimal control of each player and the optimal trajectory depending on the parameters of the described model is obtained. Full article
(This article belongs to the Special Issue Application of Game Theory)
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