Single - Valued Cores

IN THIS PAPER WE SEARCH for solutions to various classes of allocation problems. We Ž require them to be Pareto efficient and indi idually rational in the sense that no agent is . ever worse off than he would be on his own . In addition to these minimal requirements we also would like agents not to be able to profitably misrepresent their preferences. This property is known as strategy-proofness.2 Ž Two extensively analyzed classes of allocation problems are marriage problems Gale Ž .. Ž Ž .. and Shapley 1962 , and housing markets Shapley and Scarf 1974 . Results concerning Ž . strategy-proofness in marriage problems are quite disappointing. Roth 1982a shows that in the context of marriage problems there is no selection from the core correspondence Ž . that is strategy-proof. Moreover, Alcalde and Barbera 1994 show that there is no ` solution that is Pareto efficient, individually rational, and strategy-proof.3 On the other Ž . hand results pertaining to housing markets are much more encouraging. Roth 1982b shows that in the context of housing markets the core correspondence, which is shown to Ž . Ž . be single-valued by Roth and Postlewaite 1977 , is strategy-proof. Moreover Ma 1994 shows that it is the only solution that is Pareto efficient, individually rational, and strategy-proof. We search for foundations of the differences in these results. We do this by studying strategy-proofness on a general class of allocation problems that includes both models as subclasses. In addition to marriage problems and housing markets this class also includes