Applications of Differential Games and Related Models in Mathematics and Economics

A special issue of Games (ISSN 2073-4336). This special issue belongs to the section "Applied Game Theory".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 3602

Special Issue Editors


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Guest Editor
Department of Law, Economics and Human Sciences, “Mediterranea” University of Reggio Calabria, 89124 Reggio Calabria, Italy
Interests: PDEs; game theory; applied mathematics; topology
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
1. V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent 100174, Uzbekistan
2. Department of Higher and Applied Mathematics, Tashkent State University of Economics, Tashkent 100066, Uzbekistan
Interests: differential games; pursuit; evasion; optimal control; ordinary differential equations

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Guest Editor
Dipartimento Jonico in “Sistemi Giuridici ed Economici del Mediterraneo: Società Ambiente e cultura”, University "Aldo Moro" di Bari, 74121 Taranto, Italy
Interests: mathematical models for economics; finance; marketing environment; stochastic processes; optimal control; dynamic systems

Special Issue Information

Dear Colleagues,

The theme of this Special Issue is focused on differential games and the latest developments in that computational field. It is now known throughout the literature that the study of the theory of differential games has the purpose of defining the resolution of conflicting problems through the use of systems of differential equations. This area finds applications in optimal control theory and is responsible for a vast and very interesting series of ramifications in many fields of study such as graph theory, pursuit–evasion games, stochastic differential games, evolutionary games and so on in relation to defining the best strategy for the optimal solution of a conflict. The need to define differential games to address problems of natural economics lies in the fact that such games allow us to develop a multiplicity of solutions through those conceptual contributions which do not necessarily require the existence of a solution.

There are many contributions which link the theory of differential games to economics, including capital accumulation games, industrial organization and oligopoly games, marketing, resources, environmental economics, and a wide variety of other innovations. In fact, there are many examples in the literature of real applications to these economic situations.

The main objective of the Special Issue is to stimulate discussions between researchers and experts in order to define the research lines which must currently be pursued in the various parts of the world and introduce the application of differential games to fields of economics and mathematics in general.

Potential topics include but are not limited to:

  • Linear quadratic differential games;
  • Dynamic games;
  • Differential games described by PDE;
  • Applications of differential games to biology, computer science, economics, engineering, management science, operations research, and political science;
  • Hamilton–Jacobi equations for incomplete information games;
  • Continuous time games;
  • Pursuit and evasion differential games with incomplete information;
  • Hamilton–Jacobi equations in optimal control and differential games;
  • Numerical methods for differential games;
  • Control theory and theory of pursuit;
  • Pursuit–evasion differential games;
  • Stochastic pursuit–evasion differential games;
  • Evolutionary pursuit–evasion games;
  • Zero-sum differential games;
  • Pursuit–evasion games on topological spaces;
  • Pursuit and evasion differential games on graphs.

Dr. Bruno Antonio Pansera
Dr. Gafurjan Ibragimov
Dr. Lucianna Cananà
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. Games 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 1600 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

  • differential games
  • pursuit–evasion games
  • graph theory
  • topological space
  • hamilton–jacobi equations
  • numerical methods
  • PDEs

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Published Papers (3 papers)

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Research

17 pages, 530 KiB  
Article
Greenwashing Risks in Environmental Quality Competition: Detection and Deterrence
by Arka Mukherjee and Subhadip Ghosh
Games 2025, 16(2), 14; https://doi.org/10.3390/g16020014 - 11 Mar 2025
Viewed by 189
Abstract
The rising prevalence of greenwashing by firms has emerged as a major concern for regulatory authorities over the past decade. This paper examines the impact of regulation on firms’ strategic decisions regarding greenwashing and environmental quality in an oligopolistic market. We model two [...] Read more.
The rising prevalence of greenwashing by firms has emerged as a major concern for regulatory authorities over the past decade. This paper examines the impact of regulation on firms’ strategic decisions regarding greenwashing and environmental quality in an oligopolistic market. We model two firms that compete on environmental quality and greenwashing levels, operating under the oversight of a regulatory authority. The authority’s policy instruments include a detection mechanism and fines imposed on firms engaging in greenwashing. Using a differential game-theoretical framework, we examine the effectiveness of regulatory interventions like detection and penalties in reducing greenwashing behavior and enhancing environmental quality. Additionally, we discuss the post-detection trajectories of both firms, providing insights into the effects on consumer perceptions and market competition. We find that while regulation can reduce greenwashing as expected, it may also reduce firms’ environmental quality efforts. Indeed, when penalties are sufficiently high, the marginal returns on investment in greenwashing exceed those from actual green quality improvements. Full article
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6 pages, 243 KiB  
Article
Evasion Differential Games in the Space of Square Summable Sequences
by Bekhzod Aminov and Marks Ruziboev
Games 2024, 15(6), 38; https://doi.org/10.3390/g15060038 - 19 Nov 2024
Viewed by 843
Abstract
In this article, we consider simple-motion pursuit–evasion differential games in the Hilbert space of square summable sequences. We show that when the players have the same dynamic capabilities, evasion is possible under some assumptions about the initial positions of the players. Full article
6 pages, 256 KiB  
Article
Evasion Differential Game of Multiple Pursuers and a Single Evader with Geometric Constraints in 2
by Gafurjan Ibragimov, Marks Ruziboev, Ibroximjon Zaynabiddinov and Bruno Antonio Pansera
Games 2023, 14(4), 52; https://doi.org/10.3390/g14040052 - 29 Jun 2023
Cited by 2 | Viewed by 1574
Abstract
We investigate a differential evasion game with multiple pursuers and an evader for the infinite systems of differential equations in 2. The control functions of the players are subject to geometric constraints. The pursuers’ goal is to bring the state of [...] Read more.
We investigate a differential evasion game with multiple pursuers and an evader for the infinite systems of differential equations in 2. The control functions of the players are subject to geometric constraints. The pursuers’ goal is to bring the state of at least one of the controlled systems to the origin of 2, while the evader’s goal is to prevent this from happening in a finite interval of time. We derive a sufficient condition for evasion from any initial state and construct an evasion strategy for the evader. Full article
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