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Social networks with positive and negative links often split into twoantagonistic factions. Examples of such a split abound: revolutionaries versusan old regime, Republicans versus Democrats, Axis versus Allies during thesecond world war, or the Western versus the Eastern bloc during the Cold War.Although this structure, known as social balance, is well understood, it is notclear how such factions emerge. An earlier model could explain the formation ofsuch factions if reputations were assumed to be symmetric. We show this is notthe case for non-symmetric reputations, and propose an alternative model which(almost) always leads to social balance, thereby explaining the tendency ofsocial networks to split into two factions. In addition, the alternative modelmay lead to cooperation when faced with defectors, contrary to the earliermodel. The difference between the two models may be understood in terms of theunderlying gossiping mechanism: whereas the earlier model assumed that anindividual adjusts his opinion about somebody by gossiping about that personwith everybody in the network, we assume instead that the individual gossipswith that person about everybody. It turns out that the alternative model isable to lead to cooperative behaviour, unlike the previous model.

Dynamical Models Explaining Social Balance and Evolution of Cooperation