Network Formation: Bilateral Contracting and Myopic Dynamics

Abstract

We consider a network formation game where a finite number of nodes wish to send traffic to each other. Nodes contract bilaterally with each other to form bidirectional communication links; once the network is formed, traffic is routed along shortest paths (if possible). Cost is incurred to a node from four sources: (1) routing traffic; (2) maintaining links to other nodes; (3) disconnection from destinations the node wishes to reach; and (4) payments made to other nodes. We assume that a network is stable if no single node wishes to unilaterally deviate, and no pair of nodes can profitably deviate together (a variation on the notion of pairwise stability). We study such a game under a form of myopic best response dynamics. In choosing their best strategy, nodes optimize their single period payoff only. We characterize a simple set of assumptions under which these dynamics will converge to a pairwise stable network topology; we also characterize an important special case, where the dynamics converge to a star centered at a node with minimum cost for routing traffic. In this sense, our dynamics naturally select an efficient equilibrium. Further, we show that these assumptions are satisfied by a contractual model motivated by bilateral Rubinstein bargaining with infinitely patient players.