Lying Property in Balance Theory

Structural balance theory attempts to model signed networks consisting of positive (friendly) and negative (antagonistic) relations. We consider network creation games for modeling the evolution of signed networks. Recently, Malekzadeh et. al. (KDD 2011) have proposed a network creation game based on structural balance theory of signed networks. In this paper, we introduce a generalized model based on the prize collecting framework in which people can lie about their relations while all other properties of the previous model are retained. First, we prove that playing best response is NP-hard. Then, we characterize many structural properties of these networks such as upper bound of 2 for diameter, an upper bound of |V (G)|/2 for the size of a maximum independent set and lower bound of |V (G)|/2 for the degree of vertices of a Nash equilibrium graph G. By constructing tight examples, we show that all our bounds are asymptotically tight. Then, we discuss the convergence issues of the game and show that the game with any initial state will eventually converge to a Nash equilibrium in a polynomial number of rounds. In the final part of this paper, we define a new parameter Price of Lying (PoL) which shows the effects of honesty in social welfare. By experimenting our model on social networks’ real data, we show that a society without lies will be happier even if its members were fully selfish. Lying Property in Balance Theory 1