the positions they do fill are filled by foreign medical school graduates. It has been suggested that changes in the manner in which the clearinghouse treats hospitals and students might alter this situation.3 However it was shown in Roth [4] that any two outcomes that are stable-the relevant equilibrium notion4 for this kind of market-fill the same number of positions at any hospital. Since that paper also showed that the clearinghouse procedure yields a stable outcome, any change in procedure that preserves this property would thus have no effect on the perceived numerical maldistribution of physicians among hospitals. Here it is shown that any hospital that fails to fill all of its positions at some stable outcome will not only fill the same number of positions at any other stable outcome, but will fill them with exactly the same residents. Thus, while the staffs of other hospitals are determined by which of the multiple equilibria of such a market is reached, the situation of hospitals whose positions are not all filled remains unaffected. The maldistribution of phvsicians, and particularly of American educated physicians, is therefore a property of equilibria of this kind of market, and not an artifact of the particular equilibrium presently selected. The formal model:5 The agents in the hospital-intern market consist of two disjoint

[A model of job-matching is considered, in which the set of employees hired by each firm, and the set of jobs accepted by each worker, are endogenously determined, as are the job descriptions settled on by each worker-firm pair. The set of outcomes that are in equilibrium, in the sense of being stable with respect to recontracting, is shown to be nonempty. It is shown that the interests of the firms and workers are polarized over the set of stable outcomes: There exists a firm-optimal stable outcome that is the best stable outcome for every firm and the worst for every worker, and a corresponding worker-optimal stable outcome that is best for every worker and worst for very firm. These results generalize and extend previous results for models of this type, and raise questions about the nature and underlying causes of such polarization of interests.]

Two solution concepts for games without sidepayments are considered: the stable bargaining solution proposed by Harsanyi [6, 7], and the A-transfer value first proposed by Shapley [19]. Some examples of games are considered for which both solution concepts yield results which are highly counter-intuitive, and which seem to be inconsistent with the hypothesis that the games are played by rational players.

[It has recently been shown that the utility of playing a game with side payments depends on a parameter called strategic risk posture. The Shapley value is the risk neutral utility function for games with side payments. In this paper, utility functions are derived for bargaining games without side payments, and it is shown that these functions are also determined by the strategic risk posture. The Nash solution is the risk neutral utility function for bargaining games without side payments.]

It has recently been shown that the utility of playing a game with side payments depends on a parameter called strategic risk posture. The Shapley value is the risk neutral utility function for games with side payments. In this paper, utility functions are derived for bargaining games without side payments, and it is shown that these functions are also determined by the strategic risk posture. The Nash solution is the risk neutral utility function for bargaining games without side payments. RECENT WORK HAS SHOWN that the Shapley value for a game with side payments is a cardinal utility function which reflects the desirability of playing different positions in a game, or in different games (cf. Shapley [14], Roth [9]). A player's utility for playing some position in a game is determined in part by his assessment of the payoff he will receive in a class of games with side payments called bargaining games. Given a player's evaluation of these bargaining games, his utility for playing a position in any game with side payments can be determined (cf. Roth [11]). It is desirable to extend these results to games without side payments, since the assumption that side payments can be made is not appropriate in many situations. In this paper we will derive a class of utility functions for playing bargaining games without side payments. Games of this sort are studied by Nash [7], who developed a solution to bargaining games which is an extension of the Shapley value for games with side payments. That is, the Nash solution coincides with the Shapley value for bargaining games with side payments. Somewhat surprisingly, the utility of playing a bargaining game without side payments is determined by the same considerations which determine the utility of playing a game with side payments. Given a player's evaluation of bargaining games with side payments, his utility for bargaining without side payments is determined.

The Shapley value is shown to be avon Neumann-Morgenstern utility function. The concept of strategic risk is introduced, and it is shown that the Shapley value of agame equals its utility if and only if the underlying preferences are neutral to both ordinary and strategic risk.

Marketplaces are often small parts of large markets, and both markets and marketplaces come in many varieties. Market design seeks to understand what marketplaces must accomplish to enable different kinds of markets. Marketplaces can have varying degrees of success, and there can be marketplace failures. I’ll discuss labor markets like the market for new economists, and also markets for new lawyers and doctors that have suffered from the unraveling of appointment dates to well before employment begins. Markets work best if they enjoy social support, but some markets are repugnant in the sense that some people think they should be banned, even though others want to participate in them. Laws banning such markets often contribute to the design of illegal black markets, and this raises new issues for market designers. I’ll briefly discuss markets and black markets for narcotics, marijuana, sex, and surrogacy, and the design of markets for kidney transplants, in the face of widespread laws against (and broader repugnance for) compensating organ donors. I conclude with open questions and engineering challenges.