Robin Lee, NYU Stern School of Business

Markov Perfect Network Formation: An Applied Framework for Bilateral Oligopoly and Bargaining in Buyer Seller Networks

We develop a dynamic model of network formation with transfers, and detail the specification and computation of a Markov-Perfect equilibrium. Applications include the study of bilateral oligopoly and bargaining buyer-seller networks. The framework takes as primitives each agent's static profits as a function of the current network state, and computes both the equilibrium recurrent class of networks and transfers between agents. Importantly, agents anticipate future link formation and termination, and outside options when bargaining over surplus are endogenously determined to be functions of networks that will be visited in the future (including those that are not strict sub-networks). In an example drawn from healthcare, we model the negotiations between insurance firms and hospitals. Simulations reveal the efficient network may not always be realized in equilibrium, and that static Nash equilibrium conditions leveraged in previous applied work may not hold in dynamic environments leading to different predicted determinants of negotiated payments. We also demonstrate how agents' "bargaining power" and associated transfers between agents can be partially identified from observing equilibrium network structures. Finally, we use the framework to explore the impact of hospital mergers on negotiated payments, insurer premiums, and consumer welfare controlling for subsequent changes in the network and contracting partners.