An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite spaces
Basna, Rani LU
; Hilbert, Astrid
and Kolokoltsov, Vassili n
(2014)
In Communications on Stochastic Analysis
8(4).
p.449-468
- Abstract
- We investigate mean field games from the point of view of a
large number of indistinguishable players which eventually converges to infinity. The players are weakly coupled via their empirical measure. The
dynamics of the individual players is governed by pure jump type propagators over a finite space. Investigations are conducted in the framework of
non-linear Markov processes. We show that the individual optimal strategy
results from a consistent coupling of an optimal control problem with a forward non-autonomous dynamics. In the limit as the number N of players
goes to infinity this leads to a jump-type analog of the well-known non-linear
McKean-Vlasov dynamics. The case where one player has an individual... (More) - We investigate mean field games from the point of view of a
large number of indistinguishable players which eventually converges to infinity. The players are weakly coupled via their empirical measure. The
dynamics of the individual players is governed by pure jump type propagators over a finite space. Investigations are conducted in the framework of
non-linear Markov processes. We show that the individual optimal strategy
results from a consistent coupling of an optimal control problem with a forward non-autonomous dynamics. In the limit as the number N of players
goes to infinity this leads to a jump-type analog of the well-known non-linear
McKean-Vlasov dynamics. The case where one player has an individual preference different from the ones of the remaining players is also covered. The
two results combined reveal a 1
N
-Nash Equilibrium for the approximating
system of N players (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/bd891856-2a2e-459c-b5f4-1989311eecd4
- author
- Basna, Rani
LU
; Hilbert, Astrid
and Kolokoltsov, Vassili n
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- published
- in
- Communications on Stochastic Analysis
- volume
- 8
- issue
- 4
- pages
- 449 - 468
- publisher
- Serials Publications
- ISSN
- 0973-9599
- DOI
- 10.31390/cosa.8.4.02
- language
- English
- LU publication?
- no
- id
- bd891856-2a2e-459c-b5f4-1989311eecd4
- date added to LUP
- 2024-05-31 18:12:45
- date last changed
- 2024-06-04 08:37:26
@article{bd891856-2a2e-459c-b5f4-1989311eecd4,
abstract = {{We investigate mean field games from the point of view of a<br/>large number of indistinguishable players which eventually converges to infinity. The players are weakly coupled via their empirical measure. The<br/>dynamics of the individual players is governed by pure jump type propagators over a finite space. Investigations are conducted in the framework of<br/>non-linear Markov processes. We show that the individual optimal strategy<br/>results from a consistent coupling of an optimal control problem with a forward non-autonomous dynamics. In the limit as the number N of players<br/>goes to infinity this leads to a jump-type analog of the well-known non-linear<br/>McKean-Vlasov dynamics. The case where one player has an individual preference different from the ones of the remaining players is also covered. The<br/>two results combined reveal a 1<br/>N<br/>-Nash Equilibrium for the approximating<br/>system of N players}},
author = {{Basna, Rani and Hilbert, Astrid and Kolokoltsov, Vassili n}},
issn = {{0973-9599}},
language = {{eng}},
number = {{4}},
pages = {{449--468}},
publisher = {{Serials Publications}},
series = {{Communications on Stochastic Analysis}},
title = {{An epsilon-Nash equilibrium for non-linear Markov games of mean-field-type on finite spaces}},
url = {{http://dx.doi.org/10.31390/cosa.8.4.02}},
doi = {{10.31390/cosa.8.4.02}},
volume = {{8}},
year = {{2014}},
}