Differential Games and Its Applications, 2nd Edition

Dear Colleagues,

The theme of this Special Issue is focused on differential games and their latest developments. The theory of differential games finds application in conflict problems which are treated through the use of differential equations. This problem lies between classical game theory, in which multiple players are involved, and controlled dynamic systems, in which differential equations describing the game are controlled by players. In fact, such games are among the most widespread, challenging, and important optimization problems facing mobile agents. In this context, games of pursuit and evasion play a strategic role, involving one or more pursuers and one or more evaders as players. Evidently, the purposes of the groups of players are diametrically opposed: the former wants to capture the latter, and the latter wants to not be captured by the former. The strategies defined in these classes of games appear complicated, as alongside the resolution of the mathematical problem, there is that of the complex sensorimotor coordination that the pursuer must have toward the physical environment in which the pursuit takes place and the hostile behavior of the evader. There is a wide area of application for these games, ranging from simple traffic control in the rush hour of a large city to military strategies, such as missile guidance systems formulated by Rufus Isaacs, to surgery and management, and there are different kinds of hunting escape games, such as dynamic zero-sum games, instant games optimized for time, and so on. Within games where the evolution of strategies depends on continuous time, it is also necessary to remember differential games with incomplete information.

Given the numerous studies that have been carried out in this area of research, in compliance with this aim, we are interested in articles that explore various aspects of differential games and also dynamics models.

Potential topics include but are not limited to:

• Differential games of pursuit and evasion;
• Games for dynamic equations on time scales;
• Two-person zero-sum differential games;
• 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;
• Deterministic and stochastic differential games with partial observation;
• Links between incomplete information games in continuous time and repeated time games;
• Hamilton–Jacobi equations for incomplete information games;
• Continuous time games;
• Pursuit and evasion differential games with incomplete information;
• Differential games on graphs;
• Hamilton–Jacobi equations in optimal control and differential games;
• Stochastic differential games;
• Evolutionary games;
• Differential games described by the infinite system of differential equations;
• Numerical methods for differential games.

Dr. Bruno Antonio Pansera
Prof. Dr. Massimiliano Ferrara
Prof. Dr. Luca Guerrini
Dr. Tiziana Ciano
Guest Editors

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• differential games
• pursuit–evasion games
• dynamic games
• Hamilton–Jacobi equations
• numerical methods

• Differential Games and Its Applications in Mathematics (8 articles)