Cooperation and balance in signed networks: A model of multiplex formation

Abstract

We propose a game theoretic model for multiplexity in signed networks through strategic interactions amongst $n$ players who are linked to each other in an existing signed network of friendships and enmities $g$, which shape the incentive structure faced by players in their pairwise interactions with each other. These interactions take the form of simultaneous move cooperation games of complete information, wherein network effects create incentives to cooperate due to the presence of common friends as well common enemies. The set of pure strategy Nash equilibria in the strategic interactions between players $i$ and $j$ determine the nature of the tie between them in $G\left(g\right)$, which is the new layer of the signed multiplex. We investigate how properties of structural balance in the existing signed social network $g$ influence balance in the new signed network $G\left(g\right)$, identifying conditions on the existing network that yield a structurally balanced new layer of the multiplex.