Alesina and Tabellini (2007) investigate the normative criteria for allocating policy tasks to bureaucrats versus politicians. While they establish criteria with respect to a number of parameters, they do not give a criterion with respect to the degree of imperfect monitoring. We establish an unambiguous criterion about imperfect monitoring.

The theory of two-sided matching markets has interested researchers for its theoretical appeal and relevance to real-life applications. The matching of medical residents and hospitals in the United States has been studied extensively by Alvin E. Roth (1984) and others. The National Resident Matching Program (NRMP), the matching authority in the US hospital-resident matching market, runs a centralized matching mechanism that is a variant of the deferred acceptance algorithm of David Gale and Lloyd S. Shapley (1962), redesigned by Roth and Elliott Peranson (1999). A recent antitrust case against the NRMP charged that the centralized matching mechanism suppressed wages of residents. Although the lawsuit itself was dismissed, it sparked discussion about the effect of centralized matching on wages and efficiency. Jeremy Bulow and Jonathan Levin (2006, BL henceforth) investigate a matching market with price competition where each firm can hire only one worker and show that (a) the average wage is lower, (b) profit of each firm is higher, (c) wages are more compressed, and (d) the resulting matching is slightly less efficient in the presence of the matching mechanism than in any competitive equilibrium. Although BL declare “we have chosen our assumptions for analytical simplicity and transparency, not as the most realistic possible model of the residency match” (654), these results were often interpreted as an argument against the NRMP and led to discussion about potential changes of the matching mechanism. Vincent P. Crawford (forthcoming), for instance, proposes the “Flexible-Salary Match,” in which hospitals are allowed to indicate several levels of possible wages, and medical students are allowed to express preferences over pairs of hospitals and wages. We show that conclusions (a) and (b) above do not necessarily hold when firms may hire more than one worker and the number of workers in different firms are different. More specifically, we present an example with multiple positions in which the average worker wage is higher in the equilibrium with the matching mechanism than in a competitive equilibrium; and profit of each firm is lower in the equilibrium with the matching mechanism than in a competitive equilibrium. Our findings may explain why some of the results of BL disagree with empirical findings of Muriel Niederle and Roth (2003, 2004), who find little or no effect of the centralized matching on wages in some medical matching markets in the United States. Note that different firms hire different numbers of workers in many labor markets like the NRMP. There are other reasons why the conclusions and policy implications of BL may not be applicable to markets like the NRMP. For example, a competitive equilibrium may not be a

The deferred acceptance algorithm is often used to allocate indivisible objects when monetary transfers are not allowed. We provide two characterizations of agent-proposing deferred acceptance allocation rules. Two new axioms, individually rational monotonicity and weak Maskin monotonicity, are essential to our analysis. An allocation rule is the agent-proposing deferred acceptance rule for some acceptant substitutable priority if and only if it satisfies non-wastefulness and individually rational monotonicity. An alternative characterization is in terms of non-wastefulness, population monotonicity and weak Maskin monotonicity. We also offer an axiomatization of the deferred acceptance rule generated by an exogenously specified priority structure. We apply our results to characterize efficient deferred acceptance rules. 1.

The random priority (random serial dictatorship) mechanism is a common method for assigning objects. The mechanism is easy to implement and strategy-proof. However, this mechanism is inefficient, because all agents may be made better off by another mechanism that increases their chances of obtaining more preferred objects. This form of inefficiency is eliminated by a mechanism called probabilistic serial, but this mechanism is not strategy-proof. Thus, which mechanism to employ in practical applications is an open question. We show that these mechanisms become equivalent when the market becomes large. More specifically, given a set of object types, the random assignments in these mechanisms converge to each other as the number of copies of each object type approaches infinity. Thus, the inefficiency of the random priority mechanism becomes small in large markets. Our result gives some rationale for the common use of the random priority mechanism in practical problems such as student placement in public schools.

Equal pay laws increasingly require that workers with different group identities doing “similar” work are paid equal wages within firm. We study such “equal pay for similar work” (EPSW) policies theoretically and test our models’ predictions empirically using evidence from a 2009 gender-based Chilean EPSW. Under EPSW, firms segregate their workforce by gender. When there are more men than women in a labor market, EPSW increases the gender wage gap.

In an earlier work (Kamada and Kojima 2015), we introduced “matching with constraints,” a two-sided matching problem in which the market is subject to feasibility constraints. That paper proposed and analyzed a possible solution to this problem and discussed various real-market applications of our results. The present paper reorganizes some of the findings from our more recent effort, based on Kamada and Kojima (2016a, b).

Real matching markets are subject to constraints. For example, the Japanese government introduced a new medical matching system in 2009 that imposes a “regional cap” in each of its 47 prefectures, which regulates the total number of medical residents who can be employed in each region. Based on Kamada and Kojima (2011), this paper studies matching markets with such constraints by examining in great detail the Japanese medical matching market. Specifically, we show that the new system introduced in 2009 has problems in terms of stability and strategy-proofness, and provide an alternative mechanism that does better.

Hatfield and Milgrom (2005) present a unified model of matching with contracts phrased in terms of hospitals and doctors, which subsumes the standard two-sided matching and some package auction models. They show that a stable allocation exists if contracts are substitutes for each hospital. They further claim that if a hospital's preferences violate the substitutes condition, there exist singleton preferences for the other hospitals and doctors such that no stable allocation exists. We show this last claim does not hold in general. We further present a weaker condition that is necessary to guarantee the existence of stable allocations.

We study stability of two-sided many-to-one matching in which firms' preferences for workers may exhibit complementarities. Although such preferences are known to jeopardize stability in a finite market, we show that a stable matching exists in a large market with a continuum of workers, provided that each firm's choice is convex and changes continuously as the set of available workers changes. We also study the existence and structure of stable matchings under preferences exhibiting substitutability and indifferences in a large market. Building on these results, we show that an approximately stable matching exists in large finite economies. We extend our framework to ensure a stable matching with desirable incentive and fairness properties in the presence of indifferences in firms' preferences.

Studying job matching in a Kelso-Crawford framework, we consider arbitrary constraints imposed on sets of doctors that a hospital can hire. We characterize all constraints that preserve the substitutes condition (for all revenue functions that satisfy the substitutes condition), a critical condition on hospitals’ revenue functions for well-behaved competitive equilibria. A constraint preserves the substitutes condition if and only if it is a “generalized interval constraint,” which specifies the minimum and maximum numbers of hired doctors, forces some hires, and forbids others. Additionally, “generalized polyhedral constraints” are precisely those that preserve the substitutes condition for all “group separable” revenue functions.