Stackelberg Equilibrium of Opinion Dynamics Game in Social Network with Two Influence Nodes

Authors

  • Mengke Zhen Saint Petersburg State University

Abstract

The alteration of opinions of individuals in groups over time is a particular common phenomenon in social life. Taking into account the influence of homogeneous members and some special influential persons, an opinion dynamics game is established. In a social network, two special influence nodes pursuing their certain goals with the process of influencing the opinions of other normal nodes in discrete time is considered. From the perspective of non-cooperation, Stackelberg equilibrium is selected as the solution of the opinion dynamics game. Given distinct information knowledge, players will derive different equilibrium strategies. The open-loop and feedback information configurations are investigated. In the two-person non-cooperative dynamic game, techniques of Pontryagin’s minimum principle and dynamic programming are adopted to derive the equilibrium levels of influence for influence nodes and the equilibrium opinions for other normal nodes in the network. To compute and compare the various equilibrium concepts under different information structures, numerical results are presented for different scenarios.

Keywords:

social network, influence, opinion dynamics, Stackelberg equilibrium

Downloads

Download data is not yet available.

References

Acemoglu, D. and A. Ozdaglar (2011). Opinion dynamics and learning in social networks. Dynamic Games and Applications, 1(1), 3–49.

Avrachenkov, K.E., A.Y. Kondratev and V.V. Mazalov (2017). Cooperative game theory approaches for network partitioning. International Computing and Combinatorics Conference, 591–602.

Barabanov, I.N., N.A. Korgin, D.A. Novikov and A.G. Chkhartishvili (2010). Dynamic models of informational control in social networks. Automation and Remote Control, 71(11), 2417–2426.

Basar, T. and G.J. Olsder (1999). Games and dynamic games. Siam: Bangkok.

Buechel, В., T. Hellmann and S. Klöβner (2015). Opinion dynamics and wisdom under conformity. Journal of Economic Dynamics and Control, 52, 240–257.

Bure, V.M., E.M. Parilina and A.A. Sedakov (2015). Consensus in social networks with heterogeneous agents and two centers of influence. “Stability and Control Processes” in Memory of VI Zubov (SCP), 2015 International Conference, 233–236.

Bure, V.M., E.M. Parilina and A.A. Sedakov (2017). Consensus in a social network with two principals. Automation and Remote Control, 78(8), 1489–1499.

Dandekar, P., A. Goel and D.T. Lee (2013). Biased assimilation, homophily, and the dynamics of polarization. Proceedings of the National Academy of Sciences, 110(15), 5791–5796.

DeGroot, M.H. (1974). Reaching a consensus. Journal of the American Statistical Association, 69(345), 118–121.

Etesami, S.R. and T. Başar (2015). Game-theoretic analysis of the Hegselmann-Krause model for opinion dynamics in finite dimensions. IEEE Transactions on Automatic Control, 60(7), 1886–1897.

Friedkin, N.E. and E.C. Johnsen (1990). Social influence and opinions. Journal of Mathematical Sociology, 15(3-4), 193–206.

Eriedkin, N.E. and E.C. Johnsen (1999). Social influence networks and opinion change. Advances in Group Processes, 16, 1–29.

Ghaderi, J. and R. Srikant (2014). Opinion dynamics in social networks with stubborn agents: Equilibrium and convergence rate. Automatica, 50(12), 3209–3215.

Golub, B. and M.O. Jackson (2010). Naive learning in social networks and the wisdom of crowds. American Economic Journal: Microeconomics, 2(1), 112–49.

Gubanov, D.A., D.A. Novikov and A.G. Chkhartishvili (2011). Informational influence and information control models in social networks. Automation and Remote Control, 72(7), 1557–1597.

Haurie, A., J.B. Krawczyk and G. Zaccour (2012). Dynamic noncooperative game theory. World Scientific Publishing Company: Singapore.

Hegselmann, R. and U. Krause (2002). Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of artificial societies and social simulation, 5(3).

Krawczyk, J.B. and M. Tidball (2006). A discrete-time dynamic game of seasonal water allocation. Journal of optimization theory and applications, 128(2), 411–429.

Sedakov, A.A. and M. Zhen (2019). Opinion dynamics game in a social network with two influence nodes. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 15(1), 118–125.

Wang, С., H. Han and J. Han (2019). A New Network Feature Affects the Intervention Performance on Public Opinion Dynamic Networks. Scientific reports, 9(1), 5089.

Zachary, W.W. (1977). An Information Flow Model for Conflict and Fission in Small Groups. Journal of Anthropological Research, 33(4), 452–473.

Downloads

Published

2022-03-09

How to Cite

Zhen, M. (2022). Stackelberg Equilibrium of Opinion Dynamics Game in Social Network with Two Influence Nodes. Contributions to Game Theory and Management, 12. Retrieved from https://gametheory.spbu.ru/article/view/13038

Issue

Section

Articles