Influence and Counter-Influence in Networks[Mécanismes d'influence et de contre-influence dans les réseaux]

We study influence competition between two players: a designer who can shape the pattern of interaction between a set of agents and influence them, and an adversary who can counter-influence these agents. Creating the network and influencing agents are both costly activities for the two players. The final opinion and the vote of the agents depend on how the two players influence them as well as the opinion of their neighbors. Agent votes determine the payoffs of the two players and to win the designer must obtain the vote of all the agents. We begin by assuming that the designer has the better influence technology, and subsequently relax this assumption. We find that optimal strategies depend on the different costs incurred by the players, as well as who has the advantage in influence technology. We also study what happens when links between agents can arise randomly with a known exogenous probability, taking away some of the designer's control over the network. We provide conditions under which the results of the benchmark model are preserved. Next, we modify two additional assumptions: (1) requiring the designer to only secure a majority of the votes, and (2) allowing the agents interact for several rounds before casting the final vote. In both cases, the designer needs fewer resources to win the game.