An approximate Nash equilibrium for pure jump Markov games of mean-field-type on continuous state space
Basna, Rani LU
; Hilbert, Astrid
and Kolokoltsov, Vassili N.
(2017)
In Stochastics
89(6-7).
p.967-993
- 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 states of the individual players is governed by a non-autonomous pure jump type semi group in a Euclidean space, which is not necessarily smoothing. Investigations are conducted in the framework of non-linear Markovian semi groups. 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... (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 states of the individual players is governed by a non-autonomous pure jump type semi group in a Euclidean space, which is not necessarily smoothing. Investigations are conducted in the framework of non-linear Markovian semi groups. 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 an epsilon-Nash Equilibrium for the N-player games.
(Less)
- author
- Basna, Rani
LU
; Hilbert, Astrid
and Kolokoltsov, Vassili N.
- publishing date
- 2017-10-03
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- -Nash equilibrium, dynamic programing, Koopman dynamics, Mean-field games, non-linear Markov processes, optimal control, pure jump Markov process
- in
- Stochastics
- volume
- 89
- issue
- 6-7
- pages
- 967 - 993
- publisher
- Taylor & Francis
- external identifiers
-
- scopus:85015257280
- ISSN
- 1744-2508
- DOI
- 10.1080/17442508.2017.1297812
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2017 Informa UK Limited, trading as Taylor & Francis Group.
- id
- 9ce44587-2c71-4d56-80f2-8e5a7e25610e
- date added to LUP
- 2024-05-14 08:48:42
- date last changed
- 2024-05-28 10:41:05
@article{9ce44587-2c71-4d56-80f2-8e5a7e25610e,
abstract = {{<p>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 states of the individual players is governed by a non-autonomous pure jump type semi group in a Euclidean space, which is not necessarily smoothing. Investigations are conducted in the framework of non-linear Markovian semi groups. 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 an epsilon-Nash Equilibrium for the N-player games.</p>}},
author = {{Basna, Rani and Hilbert, Astrid and Kolokoltsov, Vassili N.}},
issn = {{1744-2508}},
keywords = {{-Nash equilibrium; dynamic programing; Koopman dynamics; Mean-field games; non-linear Markov processes; optimal control; pure jump Markov process}},
language = {{eng}},
month = {{10}},
number = {{6-7}},
pages = {{967--993}},
publisher = {{Taylor & Francis}},
series = {{Stochastics}},
title = {{An approximate Nash equilibrium for pure jump Markov games of mean-field-type on continuous state space}},
url = {{http://dx.doi.org/10.1080/17442508.2017.1297812}},
doi = {{10.1080/17442508.2017.1297812}},
volume = {{89}},
year = {{2017}},
}