The Role of Middlemen inEfficient and Strongly Pairwise Stable Networks

We examine the strong pairwise stability concept in network formation theory under collective network benefits.Strong pairwise stability considers a pair of players to add a link through mutual consent while permitting them to unilaterally delete any subset of links under their control.We examine the properties of strongly pairwise stable networks and find that players in middleman positions, who have the power to break up the network into multiple components, play a critical role in such networks.We show that for the component-wise egalitarian rule there is no conflict between the efficient and stable networks when these middlemen have no incentive to break up the network. Finally, we examine efficiency and stability in middleman-free networks.