Competitive Equilibrium and Trading Networks: A Network Flow Approach

This paper considers a network of agents who trade indivisible goods or services via bilateral contracts. Under a substitutability assumption on preferences, it is known that a competitive equilibrium exists. In “Competitive Equilibrium and Trading Networks: A Network Flow Approach,” Candogan, Epitropou, and Vohra show how to determine equilibrium outcomes as a generalized submodular flow problem. Existence of a competitive equilibrium and its equivalence to seemingly weaker notions of stability follow directly from the optimality conditions of the flow problem. The formulation enables the authors to perform comparative statics with respect to the number of buyers, sellers, and trades. In particular, they are able to shed light on the impact of new trading opportunities on the equilibrium trades, prices, and surpluses. In addition, they present algorithms for finding competitive equilibria in trading networks and testing stability.