Bargaining and Arbitrage in Endogenous Trading Networks∗

The paper proposes an intertemporal model of bargaining among heterogeneous buyers and sellers placed on an endogenous bipartite network. First, we characterize those networks whose trading restrictions are non-binding in that the induced outcome is “arbitrage-free,” i.e. all trade is conducted at the same price. Second, we assume that the network is endogenously determined, as captured by the standard notion of pairwise stability. We prove that pairwise-stable networks always exist and, furthermore, they are also arbitrage-free. Network endogeneity, therefore, overcomes arbitrage-related frictions. We show, however, that it induces matching-related frictions in the following sense: if the procedure is decentralized, the constraints imposed by pairwise stability prevent efficient matching. This uncovers a novel tension between network stability and efficiency that, in a trading context, cannot be attributed to impatience, disagreement, or the non-removal of arbitrage opportunities.