【241109-5】GMFG_HuangMingyi_P.Caines Graphon Mean Field Games and the GMFG Equations. Caines, P. E. & Huang, M. SIAM Journal on Control and Optimization, 59(6):4373–4399, January, 2021. arXiv:2008.10216 [math]![【241109-5】GMFG_HuangMingyi_P.Caines Graphon Mean Field Games and the GMFG Equations [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks [16, 19]. Furthermore, the study of the decentralized control of such systems was initiated in [6, 7], where Graphon Mean Field Games (GMFG) and the GMFG equations were formulated for the analysis of noncooperative dynamic games on unbounded networks. In that work, existence and uniqueness results were introduced for the GMFG equations, together with an ǫ-Nash theory for GMFG systems which relates infinite population equilibria on infinite networks to finite population equilibria on finite networks. Those results are rigorously established in this paper.
@article{caines_241109-5gmfg_huangmingyi_pcaines_2021,
title = {【241109-5】{GMFG}\_HuangMingyi\_P.{Caines} {Graphon} {Mean} {Field} {Games} and the {GMFG} {Equations}},
volume = {59},
issn = {0363-0129, 1095-7138},
url = {http://arxiv.org/abs/2008.10216},
doi = {10.1137/20M136373X},
abstract = {The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks [16, 19]. Furthermore, the study of the decentralized control of such systems was initiated in [6, 7], where Graphon Mean Field Games (GMFG) and the GMFG equations were formulated for the analysis of noncooperative dynamic games on unbounded networks. In that work, existence and uniqueness results were introduced for the GMFG equations, together with an ǫ-Nash theory for GMFG systems which relates infinite population equilibria on infinite networks to finite population equilibria on finite networks. Those results are rigorously established in this paper.},
language = {en},
number = {6},
urldate = {2024-12-10},
journal = {SIAM Journal on Control and Optimization},
author = {Caines, Peter E. and Huang, Minyi},
month = jan,
year = {2021},
note = {arXiv:2008.10216 [math]},
keywords = {/unread, Mathematics - Optimization and Control},
pages = {4373--4399},
}
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