A zero-sum differential game for two opponent masses

被引：0

作者：

Fabio Bagagiolo ^{[1
]}

Rossana Capuani ^{[2
]}

Luciano Marzufero ^{[3
]}

机构：

[1] University of Trento,Department of Mathematics

[2] University of Arizona,Department of Mathematics

[3] Free University of Bozen-Bolzano,Faculty of Economics and Management

来源：

Partial Differential Equations and Applications | 2025年 / 6卷 / 3期

关键词：

Zero-sum games; Differential games; Infinite-dimensional Isaacs equation; Mass transportation; Viscosity solutions; Primary 49N70; Secondary 49N75; 49L12; 49L25; 35Q49;

D O I：

10.1007/s42985-025-00322-5

中图分类号：

学科分类号：

摘要：

We investigate an infinite dimensional partial differential equation of Isaacs’ type, which arises from a zero-sum differential game between two masses. The evolution of the two masses is described by a controlled transport/continuity equation, where the control is given by the velocity vector field. Our study is set in the framework of the viscosity solutions theory in Hilbert spaces, and we prove the uniqueness of the value functions as solutions of the Isaacs equation.

引用

共 50 条

[1] Stochastic Recursive Zero-Sum Differential Game and Mixed Zero-Sum Differential Game
Wei, Lifeng
Wu, Zhen
MATHEMATICAL PROBLEMS IN ENGINEERING, 2012, 2012
[2] A Zero-Sum Differential Game with Exit Time
Kolpakova, Ekaterina
arXiv,
[3] Recursive Zero-Sum Stochastic Differential Game
Wei Lifeng
Wu Zhen
International Conference on Intelligent Computation Technology and Automation, Vol 2, Proceedings, 2008, : 998 - 1001
[4] A Zero-Sum Differential Game with Exit Time
Kolpakova, Ekaterina
DYNAMIC GAMES AND APPLICATIONS, 2025,
[5] It Is Not A Zero-Sum Game
Liu Xinwei
China's Foreign Trade, 2018, (06) : 48 - 49
[6] Zero-sum game
Hurst, John R.
RESPIROLOGY, 2023, 28 (12) : 1170 - 1170
[7] Zero-sum game?
Hansen, Teresa
POWER ENGINEERING, 2008, 112 (07) : 54 - +
[8] Zero-sum game
Mark Buchanan
Nature Physics, 2016, 12 : 1084 - 1084
[9] Zero-sum game
Buchanan, Mark
Nature Physics, 2016, 12 (12) : 1084 - 1084
[10] A ZERO-SUM GAME
Purcell, Julius
TLS-THE TIMES LITERARY SUPPLEMENT, 2017, (5948): : 25 - 25

← 1 2 3 4 5 →