Balance and Cooperation in Signed Networks : A Model of Multiplex Formation

In this paper, we propose and analyse a game-theoretic model for multiplexity in signed networks through strategic interactions in a finite population of n players who are linked to each other in an underlying signed social network of friendships and enmities, g, through which players experience peer pressure in their interactions with each other. These interactions take the form of simultaneous move cooperation games of complete information, where peer pressure translates to incentives to cooperate or defect. We introduce a novel type of peer pressure mechanism whereby people pressure their friends to cooperate with others that they are friends with and defect on others that they are enemies with. Also, mutual cooperation with friends yields additional premium, and players experience a psychological cost when unilaterally defecting on a friend. 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(g), which is the cooperative layer of the signed multiplex.We analyse how properties of (weak/strong) structural balance in the underlying signed social network g influence balance in the resultant signed cooperative/economic network G(g), identifying conditions on the inherited and fixed social network that are necessary and sufficient for the cooperative/economic layer of the multiplex to be structurally balanced