Equilibrium Flows : Bipartite Contracts in Decentralized Markets

This article introduces a model of decentralized markets with frictions. In our framework, utility is imperfectly transferable between agents that can only trade through bipartite contracting. Economic outcomes are defined as pairs of a flow vector and a price vector.We prove the existence of a competitive equilibrium outcome and discuss its efficiency. We interpret this equilibrium in the case of indivisible commodities. Under additional assumptions and in a partial equilibrium setting, we link this result with linear programming theories of network optimization and optimal assignment. We present two methods for the computation of such an equilibrium generalizing the simplex algorithm and ∈-relaxation algorithm to extend those computation techniques to the imperfectly transferable utility settings.As an illustration, we build a model for the overnight interbank loan market with counterparty risk and collateralization costs