Social Status in Networks

We study social comparisons and status seeking in an interconnected society. Individuals take costly actions that have direct benefits and also confer social status. A new measure of interconnectedness— cohesion—captures the intensity of incentives for seeking status. Equilibria stratify players into social classes, with each class's action pinned down by cohesion. A network decomposition algorithm characterizes the highest (and most inefficient) equilibrium. Members of the largest maximally cohesive set form the highest class. Alternatively, players not belonging to sets more cohesive than the set of all nodes constitute the lowest class. Intermediate classes are identified by iterating a cohesion operator. We also characterize networks that accommodate multiple-class equilibria.