Making a Swap : Network Formation with Increasing Marginal Costs

I propose a simple theory of strategic network formation that accounts for many empirical patterns. Three elements forge the theory: i) local linking benefits, ii) convex linking costs, and iii) swap-proofness, a new refinement of pairwise stability. If players agree about who is a more desirable neighbor, then a unique swap-proof stable graph generically exists, and stability robustly begets homophily and clustering. With further assumptions on players' desire for links, stable graphs take on structures---strong hierarchies or ordered overlapping cliques---that mirror real networks in different domains. The former in particular compel a manner of behavior in certain network games, highlighting a mechanism through which status hierarchies replicate themselves across unrelated contexts. A more general existence Theorem unifies several results in the matching literature