A Consensus Problem in Mean Field Setting with Noisy Measurements of Target

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider a class a stochastic nonzero-sum games of the mean-field (MF) type where a generic player's loss function is a convex combination of two quadratic terms: The deviation of the player's action variable from a random variable (target) which the player observes in additive noise, and deviation of the action variable from the average of the actions of all the players. Statistics of all the random variables are Gaussian. For this model, we obtain analytic expressions for Nash and MF equilibria, establish uniqueness of both as well as a direct correspondence between the two, obtain precise values of the coefficient of the leading term in the approximation to the Nash equilibrium of the finite-player game as provided by the solution of the MF game, and derive the unique distribution for the MF term which turns out not to be deterministic. We also apply the results to a price model of oligopoly with a large number of firms (players).

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6521-6526
Number of pages6
Volume2018-June
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

Fingerprint

Random variables
Additive noise
Statistics

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Basar, M. T. (2018). A Consensus Problem in Mean Field Setting with Noisy Measurements of Target. In 2018 Annual American Control Conference, ACC 2018 (Vol. 2018-June, pp. 6521-6526). [8431664] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431664

A Consensus Problem in Mean Field Setting with Noisy Measurements of Target. / Basar, M Tamer.

2018 Annual American Control Conference, ACC 2018. Vol. 2018-June Institute of Electrical and Electronics Engineers Inc., 2018. p. 6521-6526 8431664.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Basar, MT 2018, A Consensus Problem in Mean Field Setting with Noisy Measurements of Target. in 2018 Annual American Control Conference, ACC 2018. vol. 2018-June, 8431664, Institute of Electrical and Electronics Engineers Inc., pp. 6521-6526, 2018 Annual American Control Conference, ACC 2018, Milwauke, United States, 6/27/18. https://doi.org/10.23919/ACC.2018.8431664
Basar MT. A Consensus Problem in Mean Field Setting with Noisy Measurements of Target. In 2018 Annual American Control Conference, ACC 2018. Vol. 2018-June. Institute of Electrical and Electronics Engineers Inc. 2018. p. 6521-6526. 8431664 https://doi.org/10.23919/ACC.2018.8431664
Basar, M Tamer. / A Consensus Problem in Mean Field Setting with Noisy Measurements of Target. 2018 Annual American Control Conference, ACC 2018. Vol. 2018-June Institute of Electrical and Electronics Engineers Inc., 2018. pp. 6521-6526
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