Applications of Differential Game and Its Related Theories 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 August 2024 | Viewed by 1094

Special Issue 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

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:

  • Differential games of pursuit and evasion;
  • 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 the pursuit;
  • Pursuit–evasion differential games;
  • Stochastic pursuit–evasion differential games;
  • Evolutionary pursuit–evasion games;
  • Zero-sum differential games; 
  • Pursuit–evasion differential games with incomplete information,
  • Pursuit–evasion games on topological spaces;
  • Pursuit and evasion differential games on graphs.

Dr. Bruno Antonio Pansera
Guest Editor

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

Published Papers (1 paper)

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Research

6 pages, 256 KiB  
Article
Evasion Differential Game of Multiple Pursuers and a Single Evader with Geometric Constraints in 2
Games 2023, 14(4), 52; https://doi.org/10.3390/g14040052 - 29 Jun 2023
Viewed by 833
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