In this paper a consensus has been constructed in a social network which is modeled by a stochastic differential game played by agents of that network. Each agent independently minimizes a cost function which represents their motives. A conditionally expected integral cost function has been considered under an agent's opinion filtration. The dynamic cost functional is minimized subject to a stochastic differential opinion dynamics. As opinion dynamics represents an agent's differences of opinion from the others as well as from their previous opinions, random influences and stubbornness make it more volatile. An agent uses their rate of change of opinion at certain time point as a control input. This turns out to be a non-cooperative stochastic differential game which have a feedback Nash equilibrium. A Feynman-type path integral approach has been used to determine an optimal feedback opinion and control. This is a new approach in this literature. Later in this paper an explicit solution of a feedback Nash equilibrium opinion is determined.

翻译：在本文中,社会网络构建了共识,社会网络的模式是该网络的代理人所玩的随机差异游戏。每个代理人独立地将代表其动机的成本功能最小化。一个有条件的预期的整体成本功能在代理人的意见过滤下得到了考虑。动态成本功能在服从一种随机差异观点动态的前提下被最小化。由于观点动态代表了代理人与其他人以及他们以前的观点的分歧,随机影响和顽固性使得它更加不稳定。一个代理人在某个时间点使用他们的意见变化率作为控制输入。这被证明是一种不合作的随机差异游戏,具有反馈纳什均衡。一个Feynman类型的路径一体化方法被用来确定最佳的反馈观点和控制。这是文献中的一种新方法。本文稍后将确定一个反馈纳什均衡观点的明确解决方案。