The organization of the labor market for medical interns and residents underwent a number of changes before taking its present form in 1951. The record of these changes and the problems that prompted them provides an unusual opportunity to study the forces at work in markets of this kind. The present paper begins with a brief history and then presents a game-theoretic analysis to explain the orderly operation and longevity of the current market, in contrast to the turmoil that characterized various earlier short-lived attempts to organize the market. An analysis is also given of some contemporary problems facing the market. A subsidiary theme of the paper concerns the history of ideas: the problems encountered in the organization of this market, and some of the solutions arrived at, anticipated the discussion of such issues in the literature of economics and game theory.

Cost allocation, Sharpley value, Preferences, Risk

The college admissions problem is perhaps the simplest model of many-to-one matching in two-sided markets, such as labor markets. The authors show that the set of stable outcomes (which is equal to the core defined by weak domination) has some surprising properties not found in models of one-to-one matching. These properties may help to explain the success that this kind of model has had in explaining empirical observations.

The growth of kidney exchange presents new challenges for the design of kidney exchange clearinghouses. The players now include directors of transplant centers, who see sets of patient-donor pairs, and can choose to reveal only difficult-to-match pairs to the clearinghouse, while withholding easy-to-match pairs to transplant locally. This reduces the number of transplants. We discuss how the incentives for hospitals to enroll all pairs in kidney exchange can be achieved, and how the concentration of hard to match pairs increases the importance of long, non-simultaneous nondirected donor chains.

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. Because the market has complementarities between applicants and between positions, the theory of simple matching markets does not apply directly. However, computational experiments show the theory provides good approximations. Furthermore, the set of stable matchings, and the opportunities for strategic manipulation, are surprisingly small. A new kind of "core convergence" result explains this; that each applicant interviews only a small fraction of available positions is important. We also describe engineering aspects of the design process.

We consider the strategic options facing workers in labor markets with centralized market clearing mechanisms such as those in the entry level labor markets of a number of professions. If workers do not have detailed information about the preferences of other workers and firms, the scope of potentially profitable strategic behavior is considerably reduced, although not entirely eliminated. Specifically, we demonstrate that stating preferences that reverse the true preference order of two acceptable firms is not beneficial in a low information environment, but submitting a truncation of the true preferences may be. This gives some insight into the successful operation of these market mechanisms.

A fundamental assumption in much of game theory and economics is that all the relevant information for determining the rational play of a game is contained in its structural description. Recent experimental studies of bargaining have demonstrated effects due to information not included in the classical models of games of complete information. The goal of the experiment reported here is to separate these effects into components that can be attributed to the possession of specific information by specific bargainers, and to assess the extent to which the observed behavior can be characterized as equilibrium behavior. The results of the experiment permit us to identify such component effects, in equilibrium, including effects that depend on whether certain information is common knowledge or not. The paper closes with some speculation on the causes of these effects.

[Recent results have shown that, for bargaining over the distribution of commodities, or other riskless outcomes, Nash's solution predicts that risk aversion is a disadvantage in bargaining. Here we consider bargaining games which may concern risky outcomes as well as riskless outcomes, and we demonstrate that, in such games, risk aversion need not always be a disadvantage in bargaining. Intuitively, for bargaining games in which potential agreements involve lotteries which have a positive probability of leaving one of the players worse off than if a disagreement had occurred, the more risk averse a player, the better the terms of the agreement which had occurred, the more risk averse a player, the better the terms of agreeement which he must be offered in order to induce him to reach an agreement, and to compensate him for the risk involved. For bargaining games whose disagreement outcome involves no uncertainty, we characterize when risk aversion is advantageous, disadvantageous, or irrelevant from the point of view of Nash's solution.]