Applications of Differential Game and Its Related Theories in Mathematics and Economics

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

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