On the efficiency of equilibria in mean-field oscillator games

Huibing Yin, Prashant G. Mehta, Sean P. Meyn, Vinayak V. Shanbhag

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

2 Citations (Scopus)

Abstract

A key question in the design of engineered competitive systems has been that of the efficiency of the associated equilibria. Yet, there is little known in this regard in the context of stochastic dynamic games in a large population regime. In this paper, we revisit a class of noncooperative games, arising from the synchronization of a large collection of homogeneous oscillators. In [1], we derived a PDE model for analyzing the associated equilibria in large population regimes through a mean field approximation. Here, we examine the efficiency of the associated mean-field equilibria with respect to a related welfare optimization problem. We construct variational problems both for the noncooperative game and its centralized counterpart and employ these problems as a vehicle for conducting this analysis. Using a bifurcation analysis, we analyze the variational solutions and the associated efficiency loss. An expression for the efficiency loss is obtained. Finally, our results are validated through detailed numerics.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 American Control Conference, ACC 2011
Pages5354-5359
Number of pages6
StatePublished - Sep 29 2011
Event2011 American Control Conference, ACC 2011 - San Francisco, CA, United States
Duration: Jun 29 2011Jul 1 2011

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2011 American Control Conference, ACC 2011
CountryUnited States
CitySan Francisco, CA
Period6/29/117/1/11

Fingerprint

Synchronization

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Yin, H., Mehta, P. G., Meyn, S. P., & Shanbhag, V. V. (2011). On the efficiency of equilibria in mean-field oscillator games. In Proceedings of the 2011 American Control Conference, ACC 2011 (pp. 5354-5359). [5991002] (Proceedings of the American Control Conference).
Yin, Huibing ; Mehta, Prashant G. ; Meyn, Sean P. ; Shanbhag, Vinayak V. / On the efficiency of equilibria in mean-field oscillator games. Proceedings of the 2011 American Control Conference, ACC 2011. 2011. pp. 5354-5359 (Proceedings of the American Control Conference).
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Yin, H, Mehta, PG, Meyn, SP & Shanbhag, VV 2011, On the efficiency of equilibria in mean-field oscillator games. in Proceedings of the 2011 American Control Conference, ACC 2011., 5991002, Proceedings of the American Control Conference, pp. 5354-5359, 2011 American Control Conference, ACC 2011, San Francisco, CA, United States, 6/29/11.

On the efficiency of equilibria in mean-field oscillator games. / Yin, Huibing; Mehta, Prashant G.; Meyn, Sean P.; Shanbhag, Vinayak V.

Proceedings of the 2011 American Control Conference, ACC 2011. 2011. p. 5354-5359 5991002 (Proceedings of the American Control Conference).

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

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Yin H, Mehta PG, Meyn SP, Shanbhag VV. On the efficiency of equilibria in mean-field oscillator games. In Proceedings of the 2011 American Control Conference, ACC 2011. 2011. p. 5354-5359. 5991002. (Proceedings of the American Control Conference).