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...d that the subsequent activity of the agents is conditioned by these meetings. This approach has been used widely in various branches of economics, as in models of search (Diamond, 1987) or matching (=-=Roth and Sotomayor, 1990-=-). However, most of these models have paid little attention to the resultant dynamics of allocations, distributions or even of populations, concentrating on the existence of stable states or, at best,...

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...m in which all men report truthfully and each woman plays a “semisincere” strategy—moving the no-match outcome up in her rank order list to just belowsthat woman’s most preferred outcome in the core (=-=Roth and Sotomayor, 1990-=-). If onesregards the reports lvsas specifying ordinal preferences over allocation-payment pairs,sthen the semi-sincere strategies described in the theorem are similar: they merely movesthe no-trade ...

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... one slot at college c1 . Since both students are assigned only one slot the algorithm terminates and assigns both students their second choices: .D(PS , f, q)=\s1c2 s2 c1+ . Clearly the matching that assigns both students their top choiceswhich is fairPareto dominates this matching. The Pareto inefficiency of multi-category serial dictatorship is apparent, given its equivalence to the GaleShapley college optimal mechanism. What about other mechanisms? Does there exist a mechanism that is both fair and Pareto efficient? The answer is unfortunately negative. An example in Roth 6 Sotomayor [13] can easily be adopted to make this point. Example 3. Let S=[s1 , s2 , s3], C=[c1 , c2], q=(qc1 , qc2)=(1, 1), T=[t1 , t2], t(c1)=t1 , t(c2)=t2 . Let preferences PS=(Ps1 , Ps2 , Ps3) and test scores f =( f s1, f s2, f s3) be as follows: c2Ps1 c1Ps1 c0 f s1=( f s1t1 , f s1 t2 )=(90, 80) c1Ps2 c2Ps2 c0 f s2=( f s2t1 , f s2 t2 )=(80, 70) c1Ps3 c2Ps3 c0 f s3=( f s3t1 , f s3 t2 )=(70, 90) First recall that any matching that is Pareto efficient should be both individually rational and non-wasteful. There are six such matchings: +1=\s1c1 s2 c2 s3 c0+ , +2=\ s1 c1 s2 c0 s3 c2+ , +3=\ s1 c2 s2 c1 s3 c0...

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...tible kidneys (as in [51]), the problem becomes an application of what is known as the roommates problem [24]. See Abeledo and Rothblum [8], Ching [13], Diamantoudi et al. [17], and Teo and Sethuraman [61]. A.E. Roth et al. / Journal of Economic Theory 125 (2005) 151–188 155 Our paper builds on the closely related recent paper by Bogomolnaia and Moulin [12]. They considered two-sided matching, i.e. matching between two sets of agents that can be specified exogenously (e.g. firms and workers), such that an agent on one side of the market can only be matched with an agent on the other side (cf. [53]), modeled as a bipartite graph, with 0–1 preferences. It was their paper that made us aware of some of the graph-theoretic results that we also use here. Our results on the egalitarian mechanism generalize their corresponding results to general, not necessarily bipartite graphs. Kidney exchange cannot be modelled as a two-sided market, since any patient with incompatible donors can potentially be matched with any other. 11 The extensions to the general case are of interest not only because of the importance of the application to kidney exchange, but also because of the insights they give into...