Socio-economic applications of finite state mean field games

被引：39

作者：

Gomes, Diogo ^{[1
]}

Velho, Roberto M. ^{[1
]}

Wolfram, Marie-Therese ^{[2
]}

机构：

[1] 4700 King Abdullah Univ Sci & Technol, Comp Elect & Math Sci & Engn Div, Thuwal 239556900, Saudi Arabia

[2] Austrian Acad Sci, Radon Inst Computat & Appl Math, A-4040 Linz, Austria

来源：

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2014年 / 372卷 / 2028期

关键词：

mean field games; finite state space; numerical methods; socio-economic applications; CENTRAL SCHEMES; CONVERGENCE;

D O I：

10.1098/rsta.2013.0405

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or consumer choice behaviour in the free market. The corresponding finite state mean field game models are hyperbolic systems of partial differential equations, for which we present and validate different numerical methods. We illustrate the behaviour of solutions with various numerical experiments, which show interesting phenomena such as shock formation. Hence, we conclude with an investigation of the shock structure in the case of two-state problems.

引用

页数：18

共 25 条

[1] Numerical discretization of boundary conditions for first order Hamilton-Jacobi equations [J].