This paper analyzes the National System of Admissions as the mechanism employed in Chile to match universities and students. This process has three stages. The first one allows matching which are individually rational. The second one is a centralized mechanism which allows stable matchings. The last one is a decentralized mechanism and its matching will not necessarily be stable. On the basis of these results, it makes some recommendation to reach stable matchings. This paper also studies situations in which the agents have no incentives to state their true preferences to the matchmaker.
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