John William Hatfield

Stability and competitive equilibrium in trading networks

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.

Strategy-proof, efficient, and nonbossy quota allocations

We consider the problem of designing a mechanism to allocate objects to agents when each agent has a quota that must be filled exactly. Agents are assumed to have responsive preferences over items. We show that the only strategy-proof, Pareto optimal, and nonbossy mechanisms are sequential dictatorships. We also show that the only strategy-proof, Pareto optimal, nonbossy, and neutral mechanisms are serial dictatorships. Since these negative results hold for responsive preferences, they hold for more general preferences as well.

Contract design and stability in many-to-many matching

We develop a model of many-to-many matching with contracts that subsumes as special cases many-to-many matching markets and buyer–seller markets with heterogeneous and indivisible goods. In our setting, substitutable preferences are sufficient to guarantee the existence of stable outcomes; moreover, in contrast to results for the setting of many-to-one matching with contracts, if any agents preferences are not substitutable, then the existence of a stable outcome can not be guaranteed.

Federal Competition and Economic Growth

We examine the question of how competition between governments within metropolitan areas affects economic growth outcomes. Using data on metropolitan statistical areas (MSAs) in the United States, we find that the number of county governments is significantly and positively correlated with the average annual growth rate of income per employee over 1969-2006. Exploiting exogenous variation in the natural topography of our MSAs to instrument for the number of county governments, we find evidence supporting a causal interpretation of the effect of inter-jurisdictional competition on economic growth. Furthermore, our estimates suggest that not accounting for the endogeneity of inter-jurisdictional competition may lead to systematic underestimation of its growth-enhancing benefits. A natural question is whether our findings merely reflect some form of reversion to the mean. Quite to the contrary, we find that higher inter-jurisdictional competition was already associated with higher income in 1969, and that the disparity only grew over the intervening 37 years.

Multilateral matching

We introduce a matching model in which agents engage in joint ventures via multilateral contracts. This approach allows us to consider production complementarities previously outside the scope of matching theory. We show analogues of the rst and second welfare theorems, and, when agents’ utilities are concave in venture participation, show that competitive equilibria exist, correspond to stable outcomes, and yield core outcomes. Competitive equilibria exist in our setting even when externalities are present. JEL classication: C78; C62; C71; D47; D85; L14; L24

Many-to-many matching with max-min preferences

We consider the many-to-many two-sided matching problem under a stringent domain restriction on preferences called the max-min criterion. We show that, even under this restriction, there is no stable mechanism that is weakly Pareto efficient, strategy-proof, or monotonic (i.e., respects improvements) for agents on one side of the market. These results imply in particular that three of the main results of Baiou and Balinski (2000) are incorrect. We also show that one of the results of Baiou and Balinski (2007) is incorrect as well.

Pairwise kidney exchange: Comment

Abstract In their recent paper, Roth et al. [Pairwise kidney exchange, J. Econ. Theory 125 (2005) 151–188] consider pairwise kidney exchanges, and show within this subset of feasible exchanges that a priority mechanism is strategy-proof. We show that this result can be broadened to allow much more general mechanisms and restrictions on the feasible set of allocations, including allowing three-way exchanges, regional specifications, and others. The key requirement is that the choice mechanism be consistent, i.e., if an allocation is chosen from some set of feasible allocations, it is also chosen from any subset of that set.

On Derivatives Markets and Social Welfare: A Theory of Empty Voting and Hidden Ownership

In the past twenty-five years, derivatives markets have grown exponentially. Large, modern derivatives markets increasingly enable investors to hold economic interests in corporations without owning voting rights, and vice versa. This leads to both empty voters — investors whose voting rights in a corporation exceed their economic interests — and hidden owners — investors whose economic interests exceed their voting rights. We present formal models that show how, when financial markets are opaque, empty voting and hidden ownership can render financial markets unpredictable, unstable, and inefficient. By contrast, we show that when financial markets are transparent, empty voting and hidden ownership have dramatically different effects: they follow predictable patterns, encourage stable outcomes, and promote efficiency. Our analysis lends insight into the operation of securities markets in general and derivatives markets in particular. It also provides a new justification for a robust mandatory disclosure regime and facilitates analysis of proposed substantive securities regulations.

Matching in networks with bilateral contracts: extended abstract

We introduce a new matching model in which firms trade goods via bilateral contracts which specify a buyer, a seller, and the terms of the exchange. This framework subsumes all classical matching models, including that of Ostrovsky [5]. The generality our model affords allows us to make two substantial contributions. First, we show that two theoretical restrictions are necessary for classical matching theory: acyclicity - no agent may both buy from and sell to another agent, even through intermediaries, an. full substitutability - upon being endowed with an additional item, an agents demand for other items is lower, both in the sense of a reduced desire to buy additional items and an increased desire to sell items he currently owns.1 If either condition is violated, then existence of stable allocations cannot be guaranteed.2 Intuitively, if a contracting relationship contains a cycle, and if a firm in the cycle has an outside option which is preferred to one contract in the cycle, then both the outside option and the complete trading cycle are unstable; the necessity of acyclicity follows. The necessity of full substitutability is more technical, but follows closely upon prior results of Hatfield and Kominers [2]. Second, in the presence of acyclicity and fully substitutable preferences, we fully generalize the key results of classical matching theory. We prove that under these conditions stable allocations correspond bijectively to fixed points of an isotone operator; Tarskis fixed point theorem then guarantees the existence of a lattice of stable allocations. We also prove a generalization of the classical rural hospitals theorem of Roth [6] and the strategy-proofness results of Hatfield and Milgrom [3] and Hatfield and Kojima [1].3 These latter results display a surprising structure which can only be elicited within a framework as general as ours: in particular, we show that the difference between the numbers of buy- and sell-contracts held, rather than the absolute number of contracts held, is invariant across stable allocations for each agent. In light of our necessity results, our work establishes a frontier of matching theory. Without acyclicity and fully substitutable preferences, stable allocations are not guaranteed to exist in general, and hence the results of classical matching theory fail. Up to the failure of these conditions, however, all of the results of classical matching theory hold.

The Economics of Debt Clearing Mechanisms

We examine the evolution of decentralized clearinghouse mechanisms from the 13th to the 18th century; in particular, we explore the clearing of non- or limitedtradable debts like bills of exchange. We construct a theoretical model of these clearinghouse mechanisms, similar to the models in the theoretical matching literature, and show that specific decentralized multilateral clearing algorithms known as rescontre, skontrieren or virement des parties used by merchants were efficient in specific historical contexts. We can explain both the evolutionary self-organizing emergence of late medieval and early modern fairs, and its robustness during the 17th and 18th century.