Farsighted manipulation and exploitation in networks

Farsighted economic agents can use their advantage to exploit their more myopic counterparts. In public goods games played on networks, such an agent will attempt to manipulate as many of his neighbors as possible to contribute to 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. For all optimal strategies, the set of absorbing effort profiles is non-empty and is generally neither a subset or a superset of the set of Nash equilibria of the static game. Optimal long-run effort profiles for the farsighted player can be reached via a simple dependence-withdrawal strategy and the farsighted player's effects on the myopic players are only felt locally. We characterize the lower and upper bounds of long-run payoffs the farsighted player can attain in a given network and examine comparative statics with respect to adding a new link. The farsighted player always benefits from linking to more opponents and is always harmed by his neighbors linking to each other.