Friends and enemies: A model of signed network formation

I propose a simple model of signed network formation, where agents make friends to extract payoffs from weaker enemies. The model thereby accounts for the interplay between friendship and alliance on one hand and enmity and antagonism on the other. Nash equilibrium configurations are such that either everyone is friends with everyone or agents can be partitioned into different sets, where agents within the same set are friends and agents in different sets are enemies. Any strong Nash equilibrium must be such that a single agent is in an antagonistic relationship with everyone else. Furthermore, I show that Nash equilibria cannot be Pareto ranked. This paper offers a game-theoretic foundation for a large body of work on signed networks, called structural balance theory, which has been studied in sociology, social psychology, bullying, international relations, and applied physics. The paper also contributes to the literature on contests and economics of conflict.