Premuneration Values and Investments in Matching Markets

Journal of Economic Theory, 2001

Do investors making complementary investments face the correct incentives, especially when they cannot contract with each other prior to their decisions? We present a two-sided matching model in which buyers and sellers make investments prior to matching. Once matched, buyer and seller bargain over the price, taking into account outside options. Efficient decisions can always be sustained in equilibrium. We characterize the inefficiencies that can arise in equilibrium and show that equilibria will be constrained efficient. We also show that the degree of diversity in a large market has implications for the extent of any inefficiency. Journal of Economic Literature Classification Numbers: C78, D41, D51.

Journal of Economic Theory, 2001

Do investors making complementary investments face the correct incentives, especially when they cannot contract with each other prior to their decisions? We present a two-sided matching model in which buyers and sellers make investments prior to matching. Once matched, buyer and seller bargain over the price, taking into account outside options. Efficient decisions can always be sustained in equilibrium. We characterize the inefficiencies that can arise in equilibrium and show that equilibria will be constrained efficient. We also show that the degree of diversity in a large market has implications for the extent of any inefficiency.

1997

We compare the performance of markets and tournaments as allocative mechanisms in an economy with borrowing constraints. The economy consists of a continuum of individuals who differ in their initial wealth and ability level. These must be assigned to a continuum of investment opportunities or inputs of different productivity. With perfect capital markets matching is efficient under both mechanisms. Markets, however, generate higher aggregate consumption because of the waste associated with the production of signals under tournaments. When borrowing constraints are present, tournaments dominate markets in terms of matching efficiency and, for sufficiently powerful signalling technologies, also in terms of aggregate consumption. 799 ps322$p850

ACM SIGecom Exchanges, 2011

This note surveys recent work in generalized matching theory, focusing on trading networks with transferable utility. In trading networks with a finite set of contractual opportunities, the substitutability of agents' preferences is essential for the guaranteed existence of stable outcomes and the correspondence of stable outcomes with competitive equilibria. Closely analogous results hold when venture participation is continuously adjustable, but under a concavity condition on agents' preferences which allows for some types of complementarity.

We study efficient and stable mechanisms in matching markets when the number of agents is large and individuals' preferences and priorities are drawn randomly. When agents' preferences are uncorrelated, then both efficiency and stability can be achieved in an asymptotic sense via standard mechanisms such as deferred acceptance and top trading cycles. When agents' preferences are correlated over objects, however, these mechanisms are either inefficient or unstable even in an asymptotic sense. We propose a variant of deferred acceptance that is asymptotically efficient, asymptotically stable and asymptotically incentive compatible. This new mechanism performs well in a counterfactual calibration based on New York City school choice data.

SSRN Electronic Journal, 2018

In matching markets, the existence of stable matchings can only be guaranteed under substantive restrictions on preferences. We investigate how these results change in large markets, which we model with a continuum of agents of each type, following the work of Aumann Aumann (1964 1964) on general equilibrium theory. We find four main results: First, in many-to-many matching with contracts, stable outcomes do not exist in general. Second, if agents on one side of the market have substitutable preferences, then a stable outcome does exist. Third, with bilateral contracts and transferable utility, competitive equilibria always exist. Fourth, in more general settings with multilateral contracts (possibly including restrictions on transfers) and no structure on the set of agents, the core is nonempty.

Journal of Economic Theory, 2015

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 first 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.

Working Papers, 2006

2013

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the conflict/coincidence of interest properties from many-to-one and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.

International Economic Review, 2012

We consider a common indivisible good allocation problem in which agents have both social and private endowments. Popular applications include student assignment to on-campus housing, kidney exchange, and particular school choice problems. In a series of experiments Chen and Sönmez (American Economic Review 92: [1669][1670][1671][1672][1673][1674][1675][1676][1677][1678][1679][1680][1681][1682][1683][1684][1685][1686] 2002) have shown that a popular mechanism from recent theory, the Top Trading Cycles (TTC) mechanism, induces a signi…cantly higher participation rate by agents with private endowments and leads to signi…cantly more e¢ cient outcomes than the most commonly used real-life mechanism, the Random Serial Dictatorship with Squatting Rights.