Farsighted Manipulation and Exploitation in Networks

Economic agents with an increased sophistication sometimes use their advantage to exploit their more naive counterparts. In public goods games played on networks, such an agent will attempt to manipulate as many of his neighbors as possible to produce the public good. We study the exploitation of a myopic population by a single farsighted player in such games. We show the existence and payoff-uniqueness of optimal farsighted strategies in every network structure. In the long run, the farsighted player's effects are only felt locally. A simple dependence-withdrawal strategy reaches the optimal outcome for every network if the starting state is unfavorable, and reaches it for every starting state if the farsighted player is linked to all opponents. We characterize the lower and upper bounds of long-run payoffs the farsighted player can attain in a given network and make comparative statics with respect to adding a new link. The farsighted player always benefits from linking to more opponents (sociability) and is always harmed by his neighbors linking to each other (jealousy)