JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Stability and Competitive Equilibrium in Trading Networks John William HatfieldUniversity of Texas at Austin Scott Duke KominersHarvard University and University of Chicago Alexandru Nichifor University of St Andrews Michael OstrovskyStanford University Alexander Westkamp Maastricht UniversityWe 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.

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We show that in general trading networks with bilateral contracts, a suitably adapted chain stability concept (Ostrovsky, 2008) is equivalent to stability (Hatfield and Kominers, 2012; Hatfield et al., 2013) if all agents' preferences are jointly fully substitutable and satisfy the Laws of Aggregate Supply and Demand. We also show that in the special case of trading networks with transferable utility, an outcome is consistent with competitive equilibrium if and only if it is not blocked by any chain of contracts. Moreover, from a computational perspective, checking whether an outcome is chain stable is substantially easier than directly checking whether an outcome is stable.

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models' definitions of substitutability to settings in which each agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. We then introduce a new class of substitutable preferences that allows us to model intermediaries with production capacity. We also prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability.

We propose a new set of mechanisms, which we call serial dictatorship mechanisms with reservation prices for the allocation of one indivisible good. We show that a mechanism ϕ satisfies minimal tradability, individual rationality, strategy-proofness, consistency, and non wasteful tie-breaking if and only if there exists a reservation price vector r and a priority ordering such that ϕ is a serial dictatorship mechanism with reservation prices based on r and . We obtain a second characterization by replacing individual rationality with non-imposition. In both our characterizations r, , and ϕ are all found simultaneously and endogenously from the properties. In addition, we show that in our model a mechanism satisfies Pareto efficiency, strategy-proofness, and consistency if and only if it is welfare equivalent to a classical serial dictatorship. Finally, we illustrate how the normative requirements governing the functioning of some real life markets and the mechanisms that these markets use are reasonably well captured by our model and results.JEL classification: C78, D47, D71

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One-sided assignment problems combine important features of two wellknown matching models. First, as in roommate problems, any two agents can be matched and second, as in two-sided assignment problems, the division of payoffs to agents is flexible as part of the solution. We take a similar approach to one-sided assignment problems as Sasaki (Int J Game Theory 24:373-397, 1995) for two-sided assignment problems, and we analyze various desirable properties of solutions including consistency and weak pairwise-monotonicity. We show that for the class of solvable one-sided assignment problems (i.e., the subset of one-sided assignment problems with a non-empty core), if a subsolution of the core satisfies [Pareto indifference and consistency] or [invariance with respect to unmatching dummy pairs, continuity, and consistency], then it coincides with the core (Theorems 1 and 2 ). However, we also prove that on the class of all one-sided assignment problems (solvable or not), no solution satisfies consistency and coincides with the core whenever the core is nonempty (Theorem 4). Finally, we comment on the difficulty in obtaining further positive results for the class of solvable one-sided assignment problems in line with Sasaki's (1995) characterizations of the core for two-sided assignment problems.

We show that in general trading networks with bilateral contracts, a suitably adapted chain stability concept (Ostrovsky, 2008) is equivalent to stability (Hatfield and Kominers, 2012;Hatfield et al., 2013) if all agents' preferences are jointly fully substitutable and satisfy the Laws of Aggregate Supply and Demand. We also show that in the special case of trading networks with transferable utility, an outcome is consistent with competitive equilibrium if and only if it is not blocked by any chain of contracts. Moreover, from a computational perspective, checking whether an outcome is chain stable is substantially easier than directly checking whether an outcome is stable.