Open AccessGame value for a pursuit-evasion differential game problem in a Hilbert space
Author(s) -
Abbas Ja’afaru Badakaya,
Aminu Sulaiman Halliru,
Jamilu Adamu
Publication year - 2022
Publication title -
journal of dynamics and games
Language(s) - English
Resource type - Journals
eISSN - 2164-6074
pISSN - 2164-6066
DOI - 10.3934/jdg.2021019
Subject(s) - differential game , mathematics , pursuit evasion , pursuer , example of a game without a value , stochastic game , sequential game , evasion (ethics) , ordinary differential equation , hilbert space , simultaneous game , mathematical economics , game theory , mathematical optimization , differential equation , pure mathematics , mathematical analysis , immune system , immunology , biology
We consider a pursuit-evasion differential game problem with countable number pursuers and one evader in the Hilbert space \begin{document}$ l_{2}. $\end{document} Players' dynamic equations described by certain \begin{document}$ n^{th} $\end{document} order ordinary differential equations. Control functions of the players subject to integral constraints. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. The stoppage time of the game is fixed and the game payoff is the distance between evader and closest pursuer when the game is stopped. We study this game problem and find the value of the game. In addition to this, we construct players' optimal strategies.