On the Efficiency of Equilibria in Mean-Field Oscillator Games
On the Efficiency of Equilibria in Mean-Field Oscillator Games
复制标题
平均场振荡博弈中均衡的效率
DOI：
10.1007/s13235-013-0100-0
复制
发表时间：
2011
影响因子：
1.5
通讯作者：
U. Shanbhag
中科院分区：
文献类型：
--
作者：
Huibing Yin;P. Mehta;Sean P. Meyn;U. Shanbhag
设计工程竞争系统的一个关键问题是相关均衡的效率损失。然而，在这方面的背景下，随机动态博弈，特别是在一个大的人口政权知之甚少。在本文中，我们重新审视了一类非合作的游戏，所产生的大量收集的异构振荡器的同步。在Yin等人（Proceedings of 2010 American control conference，pp. 1783-1790，2010）中，我们通过平均场近似导出了一个用于分析大种群状态中相关平衡的PDE模型。在这里，我们研究了相关的平均场均衡相对于相关的福利优化问题的效率。我们构造约束变分问题的非合作博弈和其集中对应，并推导出相关的非线性特征值问题。这些本征值问题的解决方案之间的关系进行观察，并允许导出效率损失的表达式。通过应用分岔分析，在假设振子共享相同频率的条件下，导出了效率损失的局部界。通过数值算例研究，在均匀频率制度的分析报表说明，类似的数值结果提供了非均匀频率制度。
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.