Opinion dynamics game in a social network with two influence nodes

Abstract

We consider an opinion dynamics game in a social network with two influence nodes. Pursuing certain goals, the influence nodes affect other members of the network by the selection of their levels of influence. Considering this model as a 2-person non-cooperative dynamic game and choosing Nash equilibrium as its solution, we find the equilibrium levels of influence for both influence nodes at any game stage. We also perform the numerical simulation for both low and high levels of players' influence on agents.

Optimal resource allocation in the difference and differential Stackelberg games on marketing networks

“…Using the denotation (7), the decomposition (8), and selecting in (15) only those terms that contain r 0 i , we receive the expression…”

“…In this case there are one or several external control agents that exert influence on the opinions of basic network agents in their interests. In the papers which are closest to this work [15], [18] their authors built and investigated linear-quadratic game theoretic models on a network with two influence nodes. In [15] the Nash equilibrium is found for two independent nodes, and in [18] a Stackelberg equilibrium for two hierarchically 142 ALEXEI KOROLEV AND GENNADY OUGOLNITSKY organized nodes is calculated.…”

“…In the papers which are closest to this work [15], [18] their authors built and investigated linear-quadratic game theoretic models on a network with two influence nodes. In [15] the Nash equilibrium is found for two independent nodes, and in [18] a Stackelberg equilibrium for two hierarchically 142 ALEXEI KOROLEV AND GENNADY OUGOLNITSKY organized nodes is calculated. In the paper [2] we present briefly our approach to the mathematical modeling of opinion control in social networks with marketing applications.…”

Two-stage network games modeling the Belt and Road Initiative

“…Social and economic interactions such as international trade, cooperation among firms, relationship between human beings, etc., can be represented by networks, where countries, firms or people communicate and are affected by connections. For instance, in [4] an opinion dynamic game in the context of a social network is considered when influence nodes may affect other members' opinions. There are different models of network formation.…”