We consider a model of influence with a set of non-strategic agents and two strategic agents. The non-strategic agents have initial opinions and are linked through a strongly connected network. Each non-strategic agent updates his opinion by taking a weighted average of the opinions of his neighbors. The two strategic agents have fixed and opposed opinions. They each form a link with a non-strategic agent in order to influence the average opinion in the network. This procedure defines a constant-sum game whose players are the strategic agents and strategies are the non-strategic agents. We focus on the existence and the characterization of pure strategy equilibria in this setting. The characterization of equilibrium emphasizes on the one hand the influenceability of target agents and on the other hand their centrality whose characterization in our context induces a new notion called intermediacy.
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