Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems

Minyi Huang; Roland P. Malhamé; Peter E. Caines

doi:10.1109/cdc.2006.377683

Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems

Minyi Huang^*, Roland P. Malhamé, Peter E. Caines

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

68 Citations (Scopus)

Abstract

We consider large population dynamic games and illuminate methodological connections with the theory of interacting particle systems. Combined with the large population modelling, a Nash Certainty Equivalence (NCE) Methodology is introduced for specifying the localized strategy selection of a given agent within the Nash equilibrium setting. The NCE methodology closely parallels that found in the study of uncontrolled interacting particle systems within the framework of the McKean-Vlasov equation [19]: for both problems the solution is derived by focussing on a single generic individual at a microscopic level and analyzing its interaction with the ensemble of the other individuals of which it is itself, in a statistical sense, a representative.

Original language	English
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4921-4926
Number of pages	6
ISBN (Print)	1424401712, 9781424401710
DOIs	https://doi.org/10.1109/cdc.2006.377683
Publication status	Published - 2006
Event	45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: 13 Dec 2006 → 15 Dec 2006

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	45th IEEE Conference on Decision and Control 2006, CDC
Country/Territory	United States
City	San Diego, CA
Period	13/12/06 → 15/12/06

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10.1109/cdc.2006.377683

Cite this

Huang, M., Malhamé, R. P., & Caines, P. E. (2006). Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 4921-4926). Article 4177530 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/cdc.2006.377683

Huang, Minyi ; Malhamé, Roland P. ; Caines, Peter E. / Nash certainty equivalence in large population stochastic dynamic games : Connections with the physics of interacting particle systems. Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc., 2006. pp. 4921-4926 (Proceedings of the IEEE Conference on Decision and Control).

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abstract = "We consider large population dynamic games and illuminate methodological connections with the theory of interacting particle systems. Combined with the large population modelling, a Nash Certainty Equivalence (NCE) Methodology is introduced for specifying the localized strategy selection of a given agent within the Nash equilibrium setting. The NCE methodology closely parallels that found in the study of uncontrolled interacting particle systems within the framework of the McKean-Vlasov equation [19]: for both problems the solution is derived by focussing on a single generic individual at a microscopic level and analyzing its interaction with the ensemble of the other individuals of which it is itself, in a statistical sense, a representative.",

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Huang, M, Malhamé, RP & Caines, PE 2006, Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems. in Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC., 4177530, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 4921-4926, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 13/12/06. https://doi.org/10.1109/cdc.2006.377683

Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems. / Huang, Minyi; Malhamé, Roland P.; Caines, Peter E.
Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc., 2006. p. 4921-4926 4177530 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We consider large population dynamic games and illuminate methodological connections with the theory of interacting particle systems. Combined with the large population modelling, a Nash Certainty Equivalence (NCE) Methodology is introduced for specifying the localized strategy selection of a given agent within the Nash equilibrium setting. The NCE methodology closely parallels that found in the study of uncontrolled interacting particle systems within the framework of the McKean-Vlasov equation [19]: for both problems the solution is derived by focussing on a single generic individual at a microscopic level and analyzing its interaction with the ensemble of the other individuals of which it is itself, in a statistical sense, a representative.

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T3 - Proceedings of the IEEE Conference on Decision and Control

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Huang M, Malhamé RP, Caines PE. Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems. In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc. 2006. p. 4921-4926. 4177530. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/cdc.2006.377683

Nash certainty equivalence in large population stochastic dynamic games: Connections with the physics of interacting particle systems

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