Strategic network formation involving social relations: Enmity and friendship

Abstract

In this paper, we propose a connection model for formation of networks having both positive and negative links. We define utility functions of a node and hence of a network by using balanced and unbalanced triads in the network. Further, using those utility functions we define strongly efficient and conditionally efficient networks. We also find sufficient conditions for which a network will be strongly/conditionally efficient. Further, we introduce pairwise stable networks having both positive and negative links. Finally, we provide certain interesting results regarding pairwise stable networks.