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

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 (fixed) signed 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, wherein people experience pressure to cooperate with the friends of their friends. 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 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(g), identifying conditions on the existing network that are sufficient for the new layer of the multiplex to be structurally balanced