### 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 language | English (US) |
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Title of host publication | Proceedings of the 2011 American Control Conference, ACC 2011 |

Pages | 5354-5359 |

Number of pages | 6 |

State | Published - Sep 29 2011 |

Event | 2011 American Control Conference, ACC 2011 - San Francisco, CA, United States Duration: Jun 29 2011 → Jul 1 2011 |

### Publication series

Name | Proceedings of the American Control Conference |
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ISSN (Print) | 0743-1619 |

### Other

Other | 2011 American Control Conference, ACC 2011 |
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Country | United States |

City | San Francisco, CA |

Period | 6/29/11 → 7/1/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2011 American Control Conference, ACC 2011*(pp. 5354-5359). [5991002] (Proceedings of the American Control Conference).

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*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.

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

TY - GEN

T1 - On the efficiency of equilibria in mean-field oscillator games

AU - Yin, Huibing

AU - Mehta, Prashant G.

AU - Meyn, Sean P.

AU - Shanbhag, Vinayak V.

PY - 2011/9/29

Y1 - 2011/9/29

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80053144601&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053144601&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:80053144601

SN - 9781457700804

T3 - Proceedings of the American Control Conference

SP - 5354

EP - 5359

BT - Proceedings of the 2011 American Control Conference, ACC 2011

ER -