Preference revelation games and strong cores of allocation problems with indivisibilities∗

This note considers the equilibrium outcomes of the preference revelation games in the general model of indivisible good allocation introduced by Sönmez (1999). We adopt the concepts of coalitional equilibria and cores which are both defined in terms of the weak deviation or blocking by a prescribed class of admissible coalitions. We prove that if the solution which induces preference revelation games is individually rational and Pareto optimal and the class of admissible coalitions is “monotonic, ” then the set of coalitional equilibrium outcomes coincides with the core. And we point out that the preceding analysis in the context of marriage problems (Gale and Shapley, 1962) is hardly extended to the general model