Ph. D. Project
Dynamics of multi-agent systems in presence of external influencers in competition
2020/10/01 - 2023/09/30
Other supervisor(s):
Context and objective: The subject is mainly motivated by the viral marketing over social networks. The opinion evolves in time under the influence of other individuals such as friends or colleagues. The interactions between individuals take place over physical or digital networks, in the second case we speak about digital social networks. The formal analysis of opinion dynamics over social networks is an active domain of research that receives an increasing attention in the control community. The literature on the modeling of opinion dynamics in social networks is quite rich (we cite here just two seminal works [1],[2]) but it mainly treats just scenarios in which individuals are not exogenously influenced by advertisers with conflicting interests. Nevertheless this last scenario is very present in our daily life. A simple example that can be encountered in politics is the one of elections with several candidates competing for the same position. Another example is given by companies in competition to gain a market share for their products (Samsung/Apple). In this examples the individuals are influenced both by other agents and external advertisers.
Workplan: After the publication of few joint works [3], and several work meetings, the two supervisors clearly identified several non-trivial technical problems that have to be solved in order to propose a formal framework for this topic.
1) While several marketers compete to gain a market share over a social network we have to ask whether an equilibrium of the overall dynamics exists. Each marketer has to allocate its budget in space (between agents) and in time (between different campaigns for instance) in order to optimize its own cost. For this we want to analyze different types of game and opinion dynamics models. It will be of particular interest to study the effect of tensions between marketers on the behavior of opinion dynamics.
2) In a second step we want to revise the opinion dynamics models under consideration in order to include the propagation of beliefs. In other words we want to analyze the fiability of the information exchanged and the dynamics of the confidence that individuals give.

List of references

[1] M. H. DeGroot. Reaching a consensus. Journal of the American Statistical Association, 69(345):118-121, 1974.
[2] N. E. Friedkin, E. C. Johnsen. Social influence and opinions. Journal of Mathematical Sociology. 5(3-4), pp. 193-206, 1990.
[3] V. S. Varma, I.-C. Morarescu, S. Lasaulce, S. Martin. Opinion dynamics aware marketing strategies in duopolies. IEEE CDC 2017.
[4] I.-C. Morãrescu, V.S. Varma, L. Busoniu, S. Lasaulce - Space-Time Budget Allocation for Marketing Over Social Networks. 6th IFAC Conference on Analysis and Design of Hybrid Systems, Oxford, UK.
[5] V.S. Varma, I.-C. Morãrescu, S. Lasaulce, S. Martin - Marketing resource allocation in duopolies over social networks. IEEE Control Systems Letters (L-CSS), Vol. 2, No.4, 593-598, 2018.
[6] V.S. Varma, S. Lasaulce, J. Mounthanyvong, I.-C. Morãrescu - Allocating marketing resources over social networks: A long-term analysis. IEEE Control Systems Letters (L-CSS),Vol. 3, No.4, 1002-1007, 2019.
Multi-agent dynamics, opinion dynamics, game theory
Duration: 3 years
Employer: University of Lorraine
Candidate profile: The candidate should have a good mathematical background and good skills in control theory.
Control Identification Diagnosis
Doctoral contract UL