This paper considers some game-theoretic aspects of matching problems and procedures, of the sort which involve matching the members of one group of agents with one or more members of a second, disjoint group of agents, ail of whom have preferences over the possible resulting matches. The main focus of this paper is on determining the extent to which matching procedures can be designed which give agents the incentive to honestly reveal their preferences, and which produce stable matches. Two principal results are demonstrated. The first is that no matching procedure exists which always yields a stable outcome and gives players the incentive to reveal their true preferences, even though procedures exist which accomplish either of these goals separately. The second result is that matching procedures do exist, however, which always yield a stable outcome and which always give all the agents in one of the two disjoint sets of agents the incentive to reveal their true preferences.
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