On the Efficiency of Equilibria in Mean-Field Oscillator Games

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

Research output: Contribution to journalArticlepeer-review


A key question in the design of engineered competitive systems has been that of the efficiency loss of the associated equilibria. Yet, there is little known in this regard in the context of stochastic dynamic games, particularly in a large population regime. In this paper, we revisit a class of noncooperative games, arising from the synchronization of a large collection of heterogeneous oscillators. In Yin et al. (Proceedings of 2010 American control conference, pp. 1783-1790, 2010), 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 constrained variational problems both for the noncooperative game and its centralized counterpart and derive the associated nonlinear eigenvalue problems. A relationship between the solutions of these eigenvalue problems is observed and allows for deriving an expression for efficiency loss. By applying bifurcation analysis, a local bound on efficiency loss is derived under an assumption that oscillators share the same frequency. Through numerical case studies, the analytical statements are illustrated in the homogeneous frequency regime; analogous numerical results are provided for the heterogeneous frequency regime.

Original languageEnglish (US)
Pages (from-to)177-207
Number of pages31
JournalDynamic Games and Applications
Issue number2
StatePublished - Jun 2014


  • Efficiency
  • Mean-field
  • Oscillators

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Economics and Econometrics
  • Statistics and Probability
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computer Graphics and Computer-Aided Design


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