Abstract

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.

中文翻译：

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社交网络中的意见动态控制和共识

摘要

我们考虑玩家对意见动态和社交网络中达成的共识的影响的博弈论模型。控制问题是将所有参与者的意见保持在预定值附近。如果有多个玩家，那么这些目标值可能会有所不同。所考虑的动态博弈属于离散时间的线性二次博弈类。使用贝尔曼方程找到最佳控制和平衡。该解决方案以封闭形式达成。结果表明，在一个玩家的模型中，在社交网络中实现了受控共识。在有两个参与者的模型中，表明虽然社交网络中没有达成共识，但均衡完全由所有参与者的意见的平均值决定，收敛到某个值。