Opinion dynamics in social networks in presence of multiple decision-makers – NICETWEET

L'approche adoptée dans NICETWEET repose sur deux aspects fondamentaux : la dynamique d'opinion (DO) du réseau social (RS) est contrôlée, d'où le terme générique de stratégie marketing ; il peut y avoir plusieurs décideurs (DM) externes qui veulent influencer ou contrôler la DO. Ces aspects changent considérablement l'analyse de la DO et constituent des caractéristiques saillantes par rapport aux travaux connexes les plus avancés, comme expliqué ci-dessous.
Premièrement, en examinant la littérature (formelle) sur le contrôle du DO, on constate que la plupart des études existantes se concentrent sur l'analyse de modèles sans contrôle, c'est-à-dire qu'elles étudient la convergence, les modèles dynamiques ou les configurations asymptotiques de la dynamique en boucle ouverte. Le problème de la conception d'une stratégie de marketing n'est ni posé ni relié à la littérature sur le marketing viral (VM ) en économie. En revanche, dans la littérature d'économie et de marketing, le problème de la conception d'une stratégie de VM est explicitement abordé mais de manière empirique.
Deuxièmement, lorsqu'il s'agit de considérer le scénario VM le plus général de plusieurs DM, le manque de contributions formelles est encore plus évident que dans la littérature économique. contributions formelles est encore plus évident que dans le scénario d'un seul DM. Pour aborder ce nouveau scénario Pour aborder ce nouveau scénario, il faut recourir à la théorie des jeux. La théorie des jeux a été utilisée pour étudier les SNs, mais d'un point de vue différent de celui des RS. mais dans une perspective différente de la nôtre. La ligne dominante de la recherche est donnée par le problème de la formation d'opinion. formation d'opinion.

Two examples of illustrative results are given here.
Stability analysis for an adaptive DO model (LIA-CRAN-L2S): In this work, we study an instance of a continuous-time voting model on social network oriented graphs with a specific refinement: agents can break or create new links in the graph. The edges of the graph thus co-evolve with the spin (opinion) of the agents. More precisely, agents can break their links with neighbors of different spin, and create links with their neighbors' neighbors (2-hop neighbors), provided that they have the same spin. We characterize the absorbing configurations and present a special case corresponding to a single agent facing two antagonistic ideologies. By asymptotic analysis, we observe two regimes depending on the parameters of the system: in one particular regime, hesitation disappears quickly, while when the rate of link creation is sufficiently high, a slow extinction or metastability occurs. We calculate the threshold value and illustrate these results with numerical simulations. This work is a collaboration between the LIA (Y. Hayel), the CRAN (V. Varma) and the L2S (A. Berthet) within the framework of the thesis of Emmanuel Kravitzch funded by the project. Very interesting first results led to a presentation in a national conference (Roadef 2022) and to a paper submitted to an international conference (LCSS and CDC 2022).
Analysis of a game on the decentralized control of epidemics (CRAN): This work was mainly carried out by O. Lindamoulage De Silva, PhD student supervised by S. Lasaulce and I.C. Morarescu at CRAN. Even if the analysis and control of epidemics were not highlighted in the NICETWEET proposal, it can easily be seen among the potential applications. Indeed, in a first work M. Lindamoulage De Silva characterizes and analyzes the Nash equilibria of an epidemic management game. In this game the players are the decision makers in some geographical regions. They try to minimize a socio-economic cost knowing that interactions between the different regions exist and they are represented by a graph. The objective of this work is to quantify the «price of anarchy« and the «price of connectivity«. In other words, what loss of optimality in management is introduced by the decentralization of the decision as well as by the presence of interactions between the different regions. An extension of this work is currently being considered when constraints on the state of the system are imposed.

Work planned for the next period: In addition to the continuation of the above-mentioned work, new collaborations have been initiated recently on the following topics which constitute important axes for the next period:
- Analysis and ordering on platforms of trusted goods with consumer feedback (BETA-L2S-CRAN).
- Analysis of Nash equilibria for networks affected by several viruses and in the presence of several decision makers (CRAN-LIA)

Journal papers:
1. O. Lindamoulage De Silva, S. Lasaulce, I.-C. Morarescu - On the efficiency of decentralized epidemic management and application to Covid-19. IEEE L-CSS, Vol. 6, pp. 884-889, 2021.
2. E. S. Tognetti, T. R. Calliero, I.-C. Morarescu, J. Daafouz - Synchronization via output feedback for multi-agent singularly perturbed systems with guaranteed cost. Automatica, Vol. 128, 109549,2021.
3. S. Lasaulce, C. Zhang, V.S. Varma, I.-C. Morarescu - Analysis of the tradeoff between health and economic impacts of the Covid-19 epidemic. Frontiers in Public Health, Vol. 9, 620770, 2021
4. W. Yang, Y.-W. Wang, I.-C. Morãrescu, J. Daafouz- Exponential stability of singularly perturbed systems with mixed impulses. Nonlinear Analysis: Hybrid Systems, Vol. 40, 101023, 2021.
5. Bikash Adhikari, Jomphop Veetaseveera, Vineeth Varma, Irinel-Constantin Morãrescu, Elena Panteley. Computationally efficient guaranteed cost control design for clustered networks. Automatica, submitted.
Conferences:
1. Emmanuel Kravitzch, Pierre-Henri Morand, Yezekael Hayel. ProPac model: opinion-action dynamics over online social networks. Complex Networks and Applications 2021, Nov 2021, Madrid, Spain.
2. Vineeth Varma, Jomphop Veetaseveera, Romain Postoyan, Irinel-Constantin Morãrescu. Distributed gradient methods to reach a Nash equilibrium in potential games. 60th IEEE Conference on Decision and Control, CDC 2021, Dec 2021, Austin, United States.
3. Daniel Alkhorshid, Eduardo Tognetti, Irinel-Constantin Morãrescu. A bilinear systems approach with input saturation to control the agreement value of multi-agent systems. European Control Conference 2022, Jul 2022, Londre, United Kingdom
4. Sebin Gracy, Irinel-Constantin Morãrescu, Vineeth Satheeskumar Varma, Philip Paré. Analysis and On/Off Lockdown Control for Time-Varying SIS Epidemics with a Shared Resource. European Control Conference 2022, Jul 2022, Londre, United Kingdom

In the NICETWEET project, we develop a new, complete, and unified methodology to address an important and generic problem that appears in economics, finance and politics. Several decision-makers are in competition for propagating ideas or selling goods, services, etc. to a large number of agents who are connected through a physical or digital social network. The agents are thus under the (endogenous) influence of their neighbors in the social network graph but also under the exogenous influence of the decision-makers. The latter have a certain knowledge about the social network and the underlined opinion dynamics and they use it for target advertising purposes. To address this problem, we have formed an interdisciplinary team that possesses the required expertise: control theory and more specifically opinion dynamics, game theory, information theory, complex networks, and economics. In contrast with the closest works, we assume that the social network possesses new features that correspond to the economic applications of interest that are analyzed. It is very important to note that we also assume the presence of multiple decision-makers. Indeed, our preliminary knowledge about economic applications indicates that some key features need to be accounted for in a simultaneous manner. Some of these features are: the social network is often large and sparse; agents enter or leave the network randomly at any time; decision-makers may have imperfect knowledge of the social network and opinion dynamics parameters; some agents may exchange not only their opinion but also their reliability; possible presence of extremists. A salient feature with respect to the state-of-the art is that opinion dynamics over the social network can be controlled and several decision-makers try to control it. To address this problem of controlled opinion dynamics in presence of multiple decision-makers who typically have non-aligned utility functions, we will resort to game theory and contribute to bridging the gap between the formal literature of control and the typically non-formal literature of economics and marketing. More specifically, one of our technical goals is to account for the social network and opinion dynamics mathematical models to construct a formal and systematic way of designing efficient and implementable viral marketing strategies for decision-makers. One important issue in the design of viral marketing strategies is the way of allocating a given advertising, campaign, or influence budget among the social network agents and over time (in presence of competition). Efficiency will be measured in terms of using the available information by a given decision-maker and by its way of reacting to the behavior of the other decision-makers. To design viral marketing strategies in the stochastic (repeated) game framework, several approaches will be adopted in parallel to manage the risk aspect. Considering partial information about the social network and opinion dynamics, one approach will be to extract insights from the derived limiting performance characterization theorems namely, theorems that characterize the achievable long-term utilities under partial information. A step further will be to characterize equilibrium utilities and design practical equilibrium space-time budget scheduling strategies i.e., to specify exactly how a decision-maker should allocate his advertising budget among the social network agents and over time. Another approach will be to exploit multi-player learning techniques such as Bayesian learning rules tailored to the problem of interest. To implement the ambitious road-map of NICETWEET and conduct the corresponding research, recent and promising results obtained within the consortium will be exploited as a foundation of the project.