Mean field capital accumulation games: The long time behavior

Author

Minyi Huang

Author_Institution

Sch. of Math. & Stat., Carleton Univ., Ottawa, ON, Canada

fYear

2013

fDate

10-13 Dec. 2013

Firstpage

2499

Lastpage

2504

Abstract

In (Huang, Dyn. Games Appl., 2013) a mean field capital accumulation game with HARA utility was studied and by using a notion called the relaxed mean field solution it was shown that mean field dynamics in the closed-loop may exhibit stable equilibria or oscillatory (even chaotic) behavior. This paper analyzes the infinite horizon game while addressing the transient behavior of the mean field when the system dynamics can ensure predictable mean field behavior for rational agents. We analyze the associated optimal control and derive the fixed point equation for consistent mean field approximations. We further investigate numerical solutions to the coupled equation system characterizing the optimal response and the consistent mean field approximation.

Keywords

approximation theory; closed loop systems; nonlinear control systems; optimal control; stochastic games; HARA utility; associated optimal control; chaotic behavior stability; consistent mean field approximations; equilibria behavior stability; fixed point equation; hyperbolic absolute risk aversion utility; infinite horizon game; large population stochastic dynamic games; long time behavior; mean field capital accumulation games; mean field dynamics; oscillatory behavior stability; predictable mean field behavior; rational agents; relaxed mean field solution; system dynamics; Games; Jacobian matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on

Conference_Location

Firenze

ISSN

0743-1546

Print_ISBN

978-1-4673-5714-2

Type

conf

DOI

10.1109/CDC.2013.6760256

Filename

6760256