Connections between mean-field game and social welfare optimization
Connections between mean-field game and social welfare optimization
复制标题
平均场博弈与社会福利优化之间的联系
DOI：
10.1016/j.automatica.2019.108590
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Lin Zhao
中科院分区：
文献类型：
--
作者：
Sen Li;Wei Zhang;Lin Zhao
本文研究了一类平均场对策与一个社会福利优化问题之间的关系。我们考虑具有大量代理的函数空间中的平均场博弈，每个代理寻求最小化单个成本函数。不同智能体的成本函数通过依赖于布居态平均值的平均场项来耦合。我们证明了虽然平均场博弈不是势博弈，但在一定条件下，平均场博弈的ϵ-Nash均衡与一个修正的社会福利优化问题的最优解重合。这使得我们能够使用标准的最优化理论来研究平均场平衡。在此基础上，我们得到了关于平均场平衡的存在性和唯一性的新结果。我们还证明了平均场平衡可以用一种分散的原始-对偶算法来计算。数值结果验证了该方法的有效性，并通过算例说明了该方法的适用性。
This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the ϵ-Nash equilibrium of the mean-field game coincides with the optimal solution to a modified social welfare optimization problem. This enables us to study the mean-field equilibrium using standard optimization theory. Based on this connection, we derive new results on the existence and uniqueness of the mean-field equilibrium. We also show that the mean-field equilibrium can be computed by a decentralized primal–dual algorithm. Numerical results are presented to validate the solution, and examples are provided to show the applicability of the proposed approach.