Groupe d’études et de recherche en analyse des décisions

Dynamic competition over social networks

Xavier Venel École d'économie de Paris, France

"Delivering the right message to the right person at the right time" is a strong motto among in fluencers in politics, lobbying, marketing. The research until now has mainly focused on characterizing the "right person" without taking into account the "right time". The main objective of this paper is to provide a first model including this temporal dimension.

We present a model with two opposite lobbies that aim at maximizing their influence in a social network by dynamicly targeting nodes in ths network. We formulate this problem as a two-player zero-sum stochastic game and prove the existence of the uniform value: if the player are su ficiently 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-of 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 infl uence potential of agents is small, an equilibrium strategy is to systematically target the agent with the largest eigenvector centrality.

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