A model of signed network formation with heterogeneous players

This paper proposes a model of formation of signed networks that comprise both positive (friendly/cooperative) and negative (antagonistic) social ties between players who differ intrinsically in strength. Friendships/alliances serve to increase one’s power over their intrinsic strength; in the determination of power it matters not how many allies one has, but who these allies are. The model proposed here is suited to any context where players derive power from friendships/alliances with stronger players and payoffs are extracted from less powerful enemies. The structure of ties across various types of players is studied in Nash equilibria along with a characterization of Nash equilibria under various parametric conditions.