• Selected
• Entire List

Abstract:
In September 1998, the Judicial Conference of the United States abandoned its latest attempt to regulate the timing of interviews and offers in the law clerk selection process. This paper surveys the further unraveling of the market since then, makes comparisons with other entry level professional labor markets, and evaluates some possibilities for reform.

Abstract:
A great deal of late bidding has been observed on internet auctions such as eBay, which employ a second price auction with a fixed deadline. Much less late bidding has been observed on internet auctions such as those run by Amazon, which employ similar auction rules, but use an ending rule that automatically extends the auction if necessary after the scheduled close until ten minutes have passed without a bid. This paper reports an experiment that allows us to examine the effect of the different ending rules under controlled conditions, without the other differences between internet auction houses that prevent unambiguous interpretation of the field data. We find that the difference in auction ending rules is sufficient by itself to produce the differences in late bidding observed in the field data. The experimental data also allow us to examine how individuals bid in relation to their private values, and how this behavior is shaped by the different opportunities for learning provided in the auction conditions.

Abstract:
In the past, judges have often hired applicants for judicial clerkships as early as the beginning of the second year of law school for positions commencing approximately two years down the road. In the new hiring regime for federal judicial law clerks, by contrast, judges are exhorted to follow a set of start dates for considering and hiring applicants during the fall of the third year of law school. Using the same general methodology as we employed in a study of the market for federal judicial law clerks conducted in 1998-2000, we have broadly surveyed both federal appellate judges and law students about their experiences of the new market for law clerks. This paper analyzes our findings within the prevailing economic framework for studying markets with tendencies toward early hiring. Our data make clear that the movement of the clerkship market back to the third year of law school is highly valued by judges, but we also find that a strong majority of the judges responding to our surveys has concluded that nonadherence to the specified start dates is very substantial -- a conclusion we are able to corroborate with specific quantitative data from both judge and student surveys. The consistent experience of a wide range of other markets suggests that such nonadherence in the law clerk market will lead to either a reversion to very early hiring or the use of a centralized matching system such as that used for medical residencies. We suggest, however, potential avenues by which the clerkship market could stabilize at something like its present pattern of mixed adherence and nonadherence, thereby avoiding the complete abandonment of the current system.

Abstract:
In the past, judges have often hired applicants for judicial clerkships as early as the beginning of the second year of law school, for positions commencing approximately two years down the road. In the new hiring regime for federal judicial law clerks, by contrast, judges are exhorted to follow a set of start dates for considering and hiring applicants during the fall of the third year of law school. Using the same general methodology as we employed in a study of the market for federal judicial law clerks conducted in 1998-2000, we have broadly surveyed both federal appellate judges and law students about their experiences of the new market for law clerks. This Article analyzes our findings within the prevailing economic framework for studying markets with tendencies toward early hiring - a framework we both draw upon and modify in the course of our analysis. Our data make clear that the movement of the clerkship market back to the third year of law school is highly valued by judges, but we also find that a strong majority of the judges responding to our surveys has concluded that non-adherence to the specified start dates is very substantial - a conclusion we are able to corroborate with specific quantitative data from both judge and student surveys. The consistent experience of a wide range of other markets suggests that such non-adherence in the law clerk market will lead to either a reversion to very early hiring or the use of a centralized matching system such as that used for medical residencies. We suggest, however, potential avenues by which the clerkship market could stabilize at something like its present pattern of mixed adherence and non-adherence, thereby avoiding the complete abandonment of the current system.

Judicial clerkships, judges

Abstract:
In September of 1998, the Judicial Conference of the United States abandoned as unsuccessful the attempt - the sixth since 1978 - to regulate the dates at which law students are hired as clerks by Federal appellate judges. The market promptly resumed the unraveling of appointment dates that had been temporarily slowed by these efforts. In the academic year 1999-2000 many judges hired clerks in the fall of the second year of law school, almost two years before employment would begin, and before hardly any information about candidates other than first year grades was available. In an attempt to stop the further unraveling of appointment dates, a reform that has been implemented for the 2001 market is a web based public database of judges' hiring plans. Another reform that has been debated is a centralized clearinghouse modeled on the medical match. The present paper explores both these potential reforms, experimentally in the laboratory, and computationally using adaptive agents learning through genetic algorithms. Some of the special features of the judge/law-clerk market - in particular the feeling among many students and judges that students must accept offers when they are made - present potential obstacles to the success of both of these reforms.

Law clerks, Market design, Experiments

Abstract:
In second price internet auctions with a fixed end time, such as those on eBay, many bidders "snipe", i.e., they submit their bids in the closing minutes or seconds of an auction. Late bids of this sort are much less frequent in auctions that are automatically extended if a bid is submitted very late, as in auctions conducted on Amazon. We propose a model of second price internet auctions, in which very late bids have a positive probability of not being successfully submitted, and show that sniping in a fixed deadline auction can occur even at equilibrium in auctions with private values, as well as in auctions with uncertain, dependent values. Sniping in
fixed-deadline auctions also arises out of equilibrium, as a best reply to incremental bidding. However, the strategic advantages of sniping are eliminated or severely attenuated in auctions that apply the automatic extension rule. The strategic differences in the auction rules are reflected in the field data. There is more sniping on eBay than on Amazon, and this difference grows with experience. We also study the incidence of multiple bidding, and its relation to late bidding. It appears that one substantial cause of late bidding is as a strategic response to incremental bidding.

Abstract:
This essay examines how repugnance sometimes constrains what transactions and markets we see. When my colleagues and I have helped design markets and allocation procedures, we have often found that distaste for certain kinds of transactions is a real constraint, every bit as real as the constraints imposed by technology or by the requirements of incentives and efficiency. I'll first consider a range of examples, from slavery and indentured servitude (which once were not as repugnant as they now are) to lending money for interest (which used to be widely repugnant and is now not), and from bans on eating horse meat in California to bans on dwarf tossing in France. An example of special interest will be the widespread laws against the buying and selling of organs for transplantation. The historical record suggests that while repugnance can change over time, change can be quite slow.

Abstract:
This essay examines how repugnance sometimes constrains what transactions and markets we see. When my colleagues and I have helped design markets and allocation procedures, we have often found that distaste for certain kinds of transactions is a real constraint, every bit as real as the constraints imposed by technology or by the requirements of incentives and efficiency. I'll first consider a range of examples, from slavery and indentured servitude (which once were not as repugnant as they now are) to lending money for interest (which used to be widely repugnant and is now not), and from bans on eating horse meat in California to bans on dwarf tossing in France. An example of special interest will be the widespread laws against the buying and selling of organs for transplantation. The historical record suggests that while repugnance can change over time, change can be quite slow.

repugnance, market design, organ transplants, kidney exchange

Abstract:
Most business-to-business (B2B) auctions are used to transact large quantities of homogeneous goods, and therefore use multiunit mechanisms. In the B2B context, bidders often have increasing returns to scale, or synergies. We compare two commonly used auction formats for selling multiple homogeneous objects, both sometimes called Dutch auctions, in a set of value environments that include synergies and potentially subject bidders to the exposure and free-riding problems. We find that the descending-price auction, best known for its use in the Dutch flower auctions, is robust and performs well in a variety of environments, although there are some situations in which the ascending uniform-price auction similar to the one used by eBay better avoids the free-riding problem. We discuss the factors that influence each mechanism's performance in terms of the overall efficiency, the informational requirements, the seller's revenue, and the buyer's profit.

multiunit auctions, procurement auctions, supply chain management, experimental economics

Abstract:
There is a great deal of late bidding on internet second price auctions. We show that this need not result from either common value properties of the objects being sold, or irrational behavior: late bidding can occur at equilibrium even in private value auctions. The reason is that very late bids have a positive probability of not being successfully submitted, and this opens a way for bidders to implicitly collude, and avoid bidding wars, in auctions such as those run by eBay, which have a fixed end time. A natural experiment is available because the auctions on Amazon, while operating under otherwise similar rules, do not have a fixed end time, but continue if necessary past the scheduled end time until ten minutes have passed without a bid. The strategic differences in the auction rules are reflected in the auction data by significantly more late bidding on eBay than on Amazon. Furthermore, more experienced bidders on eBay submit late bids more often than do less experienced bidders, while the effect of experience on Amazon goes in the opposite direction. On eBay, there is also more late bidding for antiques than for computers. We also find scale independence in the distribution over time of bidders' last bids, of a form strikingly similar to the deadline effect' noted in bargaining: last bids are distributed according to a power law. The evidence suggests that multiple causes contribute to late bidding, with strategic issues related to the rules about ending the auction playing an important role.

Abstract:
Many markets have "unraveled" and experienced inefficient, early, dispersed transactions, and subsequently developed institutions to delay transaction timing. It has previously proved difficult, however, to measure and identify the resulting efficiency gains. Prior to 1992, college football teams were matched for post-season play up to several weeks before the end of the regular season. Since 1992, the market has reorganized to postpone this matching. We show that the matching of teams affects efficiency as measured by the resulting television viewership, and that the reorganization promoted more efficient matching, chiefly as a result of the increased ability of later matching to produce "championship" games.

Two-Sided Matching, Unraveling, Assortative Matching, Efficiency, College Football

Abstract:
We propose a novel experimental design to assess how to combine predictions from a theoretical model with experimental evidence to yield new, more accurate quantitative predictions. The first step involves deriving the predictions of the theoretical model by estimating unobserved parameters. The second step involves estimating the optimal weights with which to combine the theoretical predictions with experimental evidence. This latter estimation uses a random sample of experimental tasks from the relevant space. The optimal weight to give to the theoretical prediction can be summarized by a single number - the Equivalent Number of Observations (ENO). This number has an intuitive interpretation: the prediction of the theory is as accurate as the prediction from an experiment with n = ENO observations of the task to be predicted. To demonstrate and evaluate the use of the equivalent number of observations, the paper examines popular models in two of the best-studied problems in experimental economics: individual decision-making under uncertainty and repeated play of constant sum games. The two examples show that in addition to solving applied problems, the results provide some insights concerning the interpretation of descriptive models as useful approximations.

Abstract:
Markets sometimes unravel, with offers becoming inefficiently early. Often this is attributed to competition arising from an imbalance of demand and supply, typically excess demand for workers. However this presents a puzzle, since unraveling can only occur when firms are willing to make early offers and workers are willing to accept them. We present a model and experiment in which workers' quality becomes known only in the late part of the market. However, in equilibrium, matching can occur (inefficiently) early only when there is comparable demand and supply: a surplus of applicants, but a shortage of high quality applicants.

matching, unraveling, experiments, market design, labor demand and supply

Abstract:
In July 2005 the Boston School Committee voted to replace the existing Boston school choice mechanism with a deferred acceptance mechanism that simplifies the strategic choices facing parents. This paper presents the empirical case against the previous Boston mechanism, a priority matching mechanism, and the case in favor of the change to a strategy-proof mechanism. Using detailed records on student choices and assignments, we present evidence both of sophisticated strategic behavior among some parents, and of unsophisticated strategic behavior by others. We find evidence that some parents pay close attention to the capacity constraints of different schools, while others appear not to. In particular, we show that many unassigned students could have been assigned to one of their stated choices with a different strategy under the current mechanism. This interaction between sophisticated and unsophisticated players identifies a new rationale for strategy-proof mechanisms based on fairness, and was a critical argument in Boston's decision to change the mechanism. We then discuss the considerations that led to the adoption of a deferred acceptance mechanism as opposed to the (also strategy-proof) top trading cycles mechanism.

Abstract:
In connection with an earlier paper on the exchange of live donor kidneys (Roth, Soenmez, and Uenver 2004) the authors entered into discussions with New England transplant surgeons and their colleagues in the transplant community, aimed at implementing a Kidney Exchange program. In the course of those discussions it became clear that a likely first step will be to implement pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than exchanges involving more than two pairs. Furthermore, the experience of these surgeons suggests to them that patient and surgeon preferences over kidneys should be 0-1, i.e. that patients and surgeons should be indifferent among kidneys from healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival probabilities, regardless of the closeness of tissue types between patient and donor (unless there is a rare perfect match). In the present paper we show that, although the pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patient-donor pairs and surgeons have 0-1 preferences. This class of mechanisms includes deterministic mechanisms that would accommodate the kinds of priority setting that organ banks currently use for the allocation of cadaver organs, as well as stochastic mechanisms that allow considerations of distributive justice to be addressed.

Abstract:
Most transplanted kidneys are from cadavers, but there are also substantial numbers of transplants from live donors. Recently, there have started to be kidney exchanges involving two donor-patient pairs such that each donor cannot give a kidney to the intended recipient because of immunological incompatibility, but each patient can receive a kidney from the other donor. Exchanges are also made in which a donor-patient pair makes a donation to someone on the queue for a cadaver kidney, in return for the patient in the pair receiving the highest priority for a compatible cadaver kidney when one becomes available. We explore how such exchanges can be arranged efficiently and incentive compatibly. The problem resembles some of the 'housing' problems studied in the mechanism design literature for indivisible goods, with the novel feature that while live donor kidneys can be assigned simultaneously, the cadaver kidneys must be transplanted immediately upon becoming available. In addition to studying the theoretical properties of the design we propose for a kidney exchange, we present simulation results suggesting that the welfare gains would be substantial, both in increased number of feasible live donation transplants, and in improved match quality of transplanted kidneys.

Abstract:
We report on the design of the new clearinghouse adopted by the National Resident Matching Program, which annually fills approximately 20,000 jobs for new physicians in the United States. Because that market exhibits many complementarities between applicants and between positions, the theory of simple matching markets does not apply directly. However, computational experiments reveal that the theory provides a good approximation, and furthermore the set of stable matchings, and the opportunities for strategic manipulation, are surprisingly small. A new kind of core convergence' result is presented to explain this; the fact that each applicant can interview for only a small fraction of available positions is important. We also describe in detail engineering aspects of the design process.

Abstract:
We report on the design of the new clearinghouse adopted by the National Resident Matching Program, which annually fills approximately 20,000 jobs for new physicians in the United States. Because that market exhibits many complementarities between applicants and between positions, the theory of simple matching markets does not apply directly. However, computational experiments reveal that the theory provides a good approximation, and furthermore the set of stable matchings, and the opportunities for strategic manipulation, are surprisingly small. A new kind of "core convergence" result is presented to explain this; the fact that each applicant can interview for only a small fraction of available positions is important. We also describe in detail engineering aspects of the design process.

Abstract:
Patients needing kidney transplants may have willing donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other such pairs. The situation facing such pairs resembles models of the "double coincidence of wants," and relatively few exchanges have been consummated by decentralized means. As the population of available patient-donor pairs grows, the frequency with which exchanges can be arranged will depend in part on how exchanges are organized. We study the potential frequency of exchanges as a function of the number of patient-donor pairs, and the size of the largest feasible exchange. Developing infrastructure to identify and perform 3-way as well as 2-way exchanges will have a substantial effect on the number of transplants, and will help the most vulnerable patients. Larger than 3-way exchanges have much smaller impact. Larger populations of patient-donor pairs increase the percentage of patients of all kinds who can find exchanges.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
This essay discusses some things we have learned about markets, in the process of designing marketplaces to fix market failures. To work well, marketplaces have to provide thickness, i.e. they need to attract a large enough proportion of the potential participants in the market; they have to overcome the congestion that thickness can bring, by making it possible to consider enough alternative transactions to arrive at good ones; and they need to make it safe and sufficiently simple to participate in the market, as opposed to transacting outside of the market, or having to engage in costly and risky strategic behavior. I'll draw on recent examples of market design ranging from labor markets for doctors and new economists, to kidney exchange, and school choice in New York City and Boston.

Abstract:
Many markets have organizations that influence or try to establish norms concerning when offers can be made, accepted and rejected. Examining a dozen previously studied markets suggests that markets in which transactions are made far in advance are markets in which it is acceptable for firms to make exploding offers, and unacceptable for workers to renege on commitments they make, however early. But this evidence is only suggestive, because the markets differ in many ways other than norms concerning offers. Laboratory experiments allow us to isolate the effects of exploding offers and binding acceptances. In a simple environment, in which uncertainty about applicants' quality is resolved over time, we find inefficient early contracting when firms can make exploding offers and applicants' acceptances are binding. Relaxing either of these two conditions causes matching to take place later, when more information about applicants' qualities is available, and consequently results in higher efficiency and fewer blocking pairs. This suggests that elements of market culture may play an important role in influencing market performance.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
New gastroenterologists participated in a labor market clearinghouse (a "match") from 1986 through the late 1990's, after which the match was abandoned. This provides an opportunity to study the effects of a match, by observing the differences in the outcomes and organization of the market when a match was operating, and when it was not.

After the GI match ended, the market unraveled. Contracts were signed earlier each year, at diffuse times, often with exploding offers. The market became less national, more local. This allows us to discern the effect of the clearinghouse: it coordinated the timing of the market, in a way that increased its thickness and scope. The clearinghouse does not seem to have had an effect on wages.

As this became known among gastroenterologists, an opportunity arose to reorganize the market to once again use a centralized clearinghouse. However it proved necessary to adopt policies that would allow employers to safely delay hiring and coordinate on using the clearinghouse.

The market for gastroenterologists provides a case study of market failures, the way a centralized clearinghouse can fix them, and the effects on market outcomes. In the conclusion we discuss aspects of the experience of the gastroenterology labor market that seem to generalize fairly widely.

Abstract:
The deferred acceptance algorithm proposed by Gale and Shapley (1962) has had a profound influence on market design, both directly, by being adapted into practical matching mechanisms, and, indirectly, by raising new theoretical questions. Deferred acceptance algorithms are at the basis of a number of labor market clearinghouses around the world, and have recently been implemented in school choice systems in Boston and New York City. In addition, the study of markets that have failed in ways that can be fixed with centralized mechanisms has led to a deeper understanding of some of the tasks a marketplace needs to accomplish to perform well. In particular, marketplaces work well when they provide thickness to the market, help it deal with the congestion that thickness can bring, and make it safe for participants to act effectively on their preferences. Centralized clearinghouses organized around the deferred acceptance algorithm can have these properties, and this has sometimes allowed failed markets to be reorganized.

Abstract:
The collapse of the clearinghouse for the entry-level gastroenterology labor market offers a unique opportunity to study how stable clearinghouses succeed and fail. To explore the reasons for the failure of the clearinghouse (and why failures of this kind of clearinghouse have been so rare), we conduct an experimental investigation of demand shocks of the kind that occurred in the gastroenterology market. We find that a reduction in demand for positions leads to the collapse of the match only when it is detectable by firms before being detected by workers (as in the unexpected shock that took place in 1996, which could be seen by firms in their reduced applicant pools). Simple demand and supply imbalances do not seem to interfere with the operation of the centralized match. Our results suggest an affirmative answer to the question posed by market participants about whether the clearinghouse could be successfully restarted, and that this would relieve some of the distress now reported in that market, by allowing it to operate later, at a more uniform time, and with more national scope.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
Patients needing kidney transplants may have donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other pairs only when there is a "double coincidence of wants." Developing infrastructure to perform 3-way as well as 2-way exchanges will have a substantial effect on the number of transplants that can be arranged. Larger than 3-way exchanges have less impact on efficiency. In a general model of type-compatible exchanges, the size of the largest exchanges required to achieve efficiency equals the number of types.

Abstract:
From 1986 through 1997 the entry-level market for American gastroenterologists was organized by a centralized clearinghouse. Before, and since, it has been conducted via a decentralized market in which appointment dates have unraveled to well over a year before the start of employment. The career paths of gastroenterologists therefore offer a unique opportunity to examine the difference between the market when appointments are decentralized and early, versus when they are made later via a centralized clearinghouse. (Most centralized clearinghouses remain in use once established, and so there is no way to separate changes due to the clearinghouse from other changes that may have taken place over time.) We find that, both before and after the years in which the centralized clearinghouse was used, gastroenterologists are less mobile, and more likely to be employed at the same hospital in which they were internal medicine residents, than when the clearinghouse was in use. This suggests that the clearinghouse serves not only to coordinate the timing of appointments, but that it also increases the scope of the market, compared to decentralized markets with early appointments and exploding offers. This has implications for theories of market failure due to unraveling over time.

Abstract:
This article discusses some things we have learned about markets, in the process of designing marketplaces to fix market failures. To work well, marketplaces have to provide thickness, i.e. they need to attract a large enough proportion of the potential participants in the market; they have to overcome the congestion that thickness can bring, by making it possible to consider enough alternative transactions to arrive at good ones' and they need to make it safe and sufficiently simple to participate in the market, as opposed to transacting outside of the market, or having to engage in costly and risky strategic behavior. I will draw on recent examples of market design ranging from labor markets for doctors and new economists, to kidney exchange, and school choice in New York City and Boston.

Abstract:
Markets sometimes unravel, with offers becoming inefficiently early. Often this is attributed to competition arising from an imbalance of demand and supply, typically excess demand for workers. However this presents a puzzle, since unraveling can only occur when firms are willing to make early offers and workers are willing to accept them. We present a model and experiment in which workers' quality becomes known only in the late part of the market. However, in equilibrium, matching can occur (inefficiently) early only when there is comparable demand and supply: a surplus of applicants, but a shortage of high quality applicants.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
The design of the New York City (NYC) High School match involved tradeoffs among efficiency, stability and strategy-proofness that raise new theoretical questions. We analyze a model with indifferences-ties-in school preferences. Simulations with field data and the theory favor breaking indifferences the same way at every school - single tie breaking - in a student-proposing deferred acceptance mechanism. Any inefficiency associated with a realized tie breaking cannot be removed without harming student incentives. Finally, we empirically document the extent of potential efficiency loss associated with strategy-proofness and stability, and direct attention to some open questions.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
The design of the New York City (NYC) High School match involved tradeoffs between incentives and efficiency, because some schools are strategic players that rank students in order of preference, while others order students based on large priority classes. Therefore it is desirable for a mechanism to produce stable matchings (to avoid giving the strategic players incentives to circumvent the match), but is also necessary to use tie-breaking for schools whose capacity is sufficient to accommodate some but not all students of a given priority class. We analyze a model that encompasses one-sided and two-sided matching models. We first observe that breaking indifferences the same way at every school is sufficient to produce the set of student optimal stable matchings. Our main theoretical result is that a student-proposing deferred acceptance mechanism that breaks indifferences the same way at every school is not dominated by any other mechanism that is strategyproof for students. Finally, using data from the recent redesign of the NYC High School match, which places approximately 90,000 students per year, we document that the extent of potential efficiency loss is substantial. Over 6,800 student applicants in the main round of assignment could have improved their assignment in a (non strategy-proof) student optimal mechanism, if the same student preferences would have been revealed.

Abstract:
The entry-level market for American gastroenterologists was organized by a centralized clearinghouse from 1986 to 1996. Before, and since, it has been conducted via a decentralized market in which appointment dates have unraveled to well over a year before the start of employment. We find that, both before and after the years in which the centralized clearinghouse was used, gastroenterologists are less mobile and more likely to be employed at the same hospital in which they were internal medicine residents than when the clearinghouse was in use. This suggests that the clearinghouse not only coordinates the timing of appointments but also increases the scope of the market, compared to a decentralized market with early appointments.

Abstract:
In the context of entry-level labor markets, we consider the potential transactions that have to be evaluated before equilibrium transactions can be identified. These potential transactions involve offers that are rejected. After an initial phase in which many offers can be proffered in parallel, subsequent potential transactions must be processed serially, since a new offer cannot be made until an outstanding offer is rejected. In this phase even a small time required to process offers and rejections may cause bottlenecks. In many, perhaps most, decentralized labor markets, this means that transactions have to be finalized before there is time for the market to clear, that is, before all the potential transactions that would need to be evaluated in order to reach a stable outcome can in fact be evaluated. This has implications for the strategic behavior of firms and workers. In particular, in deciding to whom to offer a position, a firm may have strong incentives to consider not only its preferences over workers but also the likelihood that its offer will be accepted, since if its offer is rejected it may find that many other potential employees have become unavailable in the interim. The analysis is carried out in connection with the decentralized market for clinical psychologists. The implications for other kinds of markets are considered.