Critical agents in networks

We examine the fundamental tension between efficiency and stability in social network formation. Jackson and Wolinsky (JET, 1996) showed that the component-wise egalitarian payoff rule supports an efficient network as being pairwise stable if and only if the network benefit function is critical link monotone. We extend this insight to strong pairwise stability and derive that the critical link monotonicity condition has to be strengthened to a condition on individuals occupying critical positions in the network.