价值(数学)
数理经济学
二次方程
计算机科学
数学优化
数学
班级(哲学)
社会动力
动力学(音乐)
控制(管理)
应用数学
社交网络(社会语言学)
控制理论(社会学)
人工智能
统计
心理学
社会化媒体
教育学
万维网
几何学
作者
Chen Wang,Владимир Мазалов,Hongwei Gao
标识
DOI:10.1134/s0005117921060102
摘要
We consider a game-theoretic model of the influence of players on the dynamics of opinions
and the consensus achieved in a social network. The control problem is to maintain the opinions
of all participants in the vicinity of a predetermined value. If there are several players, then these
target values may differ. The considered dynamic game belongs to the class of linear-quadratic
games in discrete time. Optimal control and equilibrium are found using the Bellman equation.
The solution is reached in closed form. It is shown that in the model with one player, a controlled
consensus is achieved in the social network. In the model with two players, it is shown that
although there is no consensus in the social network, the equilibrium is completely determined by
the mean value of the opinions of all participants, which converges to a certain value. The results
of numerical modeling for a social network with one and two players are presented.
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