Project Abstract There are three projects making up this proposal. The first deals with the question of the stability of exchange in environments in which individuals possess private information that is relevant to others. When information is complete, economists understand well which allocations exhibit stability in the sense that agents will pursue no further trade once the allocation is established. However, to date there is no single agreed-upon notion of stability when the agents involved possess private information. Different notions of stability have been introduced in this setting and each is characterized by the structure of communication between the agents that it allows. We suggest that it might be helpful to attempt to endogenize this communication structure, thereby settling on a single, more fruitful notion of stability. Any success in this research would have practical implications for the design of trading institutions. For example, in the recent FCC spectrum auctions, the auction design may not have best taken into account the potential for resale. Similar resale issues arise as well in many government procurement activities. When such resale is desirable, it signals an instability in the outcome generated by the institution at hand (i.e., the FCC auction; or government procurement rules). The present research seeks to provide a framework within which institutions can be designed so that the outcomes they produce are not susceptible to advantageous manipulation. This will not only enhance efficiency, but it may lead to increased revenues from the sale of government-owned entities as well. The second project concerns the yearly process of matching new interns to hospitals in the US, which is carried out using a version of what is known as the Gale-Shapley algorithm. In brief, hospitals list a number of candidates, in order of preference, that they would be willing to hire for positions that are open, and interns list, again in order of preference, the hospitals they would be willing to be matched with. The essential question is this: Is the matching produced by the GS algorithm stable, in the sense that no intern-hospital pair prefers one another to their GS-algorithm matches? This project is directed at showing that in large matching markets (such as the hospital/intern market) in which the preferences of agents are private information, but are independently generated across agents on both sides of the market, there is very little room for strategic manipulation of one's reported preferences when the Gale-Shapley algorithm is employed. More precisely, it appears that when the market is large, and interns can only submit relatively short lists to the algorithm (which is the case in practice), then it is best for interns to submit truthful lists. (Surprisingly, in other circumstances it can benefit an intern to place an inferior hospital above a superior one on his list; but it is always best for hospitals to submit truthful lists). This theoretical result implies that the outcome of the GS algorithm does indeed possess the crucial stability property that is a prerequisite for maintaining its use. The third project centers on the issue of information and knowledge in the theory of implementation. An example illustrates the problem. Consider the rather common setting in which a partnership is being dissolved. How ought the jointly-owned assets be distributed among the partners? (The partners may be a divorcing husband and wife whose assets are their possessions, or the partners may be members of a law firm, whose assets are, at least in part, their clients.) In many instances, the partners do not wish to simply sell the assets and share the proceeds according to their ownership shares, but rather one or more of the partners wishes to maintain possession of the assets by paying off the other partners. Which partners should maintain possession of the assets, and how much should they compensate the others? Both answers depend upon the intrinsic value each partner places on the assets, a value known only to that partner. Determining the correct allocation and compensation is no simple task. Various institutions have arisen for handling this problem, including the `cut and choose` method, where one partner proposes a price, and the other must decide whether to buy (from the other) or sell (to the other) the assets at that price. Despite its prevalent use, this scheme has undesirable properties: when the values placed on the assets are private information, this method can result in the `wrong` partner ending up with the assets. We seek as simple a scheme as possible that can achieve an efficient and envy-free outcome in a partnership dissolution context. Since some of our previous research has already resulted in a scheme that yields an efficient (although perhaps not envy-free) outcome, we believe it is only a matter of time before the present (more important) problem is also solved.
