Stability and Competitive Equilibrium in Trading Networks

John William  Hatfield; Scott Duke Kominers; Alexandru   Nichifor; Michael  Ostrovsky; Alexander  Westkamp

Article | Journal of Political Economy

Stability and Competitive Equilibrium in Trading Networks

by John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp

Abstract

We introduce a model in which agents in a network can trade via bilateral contracts. We find that when continuous transfers are allowed and utilities are quasi-linear, the full substitutability of preferences is sufficient to guarantee the existence of stable outcomes for any underlying network structure. Furthermore, the set of stable outcomes is essentially equivalent to the set of competitive equilibria, and all stable outcomes are in the core and are efficient. By contrast, for any domain of preferences strictly larger than that of full substitutability, the existence of stable outcomes and competitive equilibria cannot be guaranteed.

Keywords: Balance and Stability; Markets;

Format: Print

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Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Stability and Competitive Equilibrium in Trading Networks." Journal of Political Economy 121, no. 5 (October 2013): 966–1001.

This paper develops a class of equilibrium-independent predictions of competitive equilibrium with indivisibilities. Specifically, we prove an analogue of the “Lone Wolf Theorem” of classical matching theory, showing that when utility is perfectly transferable, any agent who does not participate in trade in one competitive equilibrium must receive her autarky payoff in every competitive equilibrium. Our results extend to approximate equilibria and to settings in which utility is only approximately transferable.

Hatfield and Kominers (2012) introduced a model of matching in networks with bilateral contracts and showed that stable outcomes exist in supply chains when firms' preferences over contracts are fully substitutable. Hatfield and Kominers (2012) also asserted that in their setting, full substitutability is equivalent to the assumption that all indirect utility representations of each firm's preferences are quasisubmodular; we show here that this claimed equivalence result does not hold in general. We show instead that full substitutability is equivalent to weak quasisubmodularity of all indirect utility representations.

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Stability and Competitive Equilibrium in Trading Networks

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