Dynamic competition over social networks Dynamic competition over social networks

Résumé En Fr

We provide an analytical approach to the problem of influence maximization in a social network when two players compete by means of dynamic targeting strategies. We formulate the problem as a two-player zero-sum stochastic game. We prove the existence of the uniform value: if the players are sufficiently patient, both players can guarantee the same mean-average opinion without knowing the exact discount factor. Further, we put forward some elements for the characterization of equilibrium strategies. In general, players must implement a trade-off between a forward-looking perspective, according to which they shall aim at maximizing the future spread of their opinion in the network, and a backward-looking perspective, according to which they shall aim at counteracting their opponent's previous actions. When the influence potential of players is small, an equilibrium strategy is to systematically target the agent with the largest eigenvector centrality.

Nous proposons une approche analytique au problème de maximisation de l'influence dans un réseau social entre deux joueurs utilisant des stratégies dynamiques. Le problème est formulé comme un jeu stochastique à somme nulle. Nous prouvons l'existence de la valeur uniforme et donnons une caractérisation partielle des stratégies d'équilibre. Nous montrons notamment que lorsque l'influence exercée par les agents est faible, ces derniers doivent systématiquement cibler l'agent avec la centralité "vecteur propre" la plus élevée.