Tuition Exchange ∗ Umut Mert Dur † University of Texas M. Utku Ünver ‡ Boston College November 25, 2012 Abstract We introduce a new class of matching problems that mimics the tuition exchange programs employed by colleges in the US to enable the dependents of their eligible faculty to use their tuition benefits at other participating institutions. Each participating college has to maintain a balance between exported and imported students; a negative balance with exports exceeding imports is generally penalized by suspension from the program. On the other hand, these programs function through decentralized markets that make it difficult to sustain a balance. We show that any unbalanced market equilibrium respecting stability causes a race to the bottom by discouraging negative–balance colleges from exchange. To correct this failure, we propose a new centralized mechanism, two–sided top trading cycles (2S-TTC), a variant of the well–known TTC mechanism. This is the first time a one–sided matching mechanism has been modified for a two–sided market. This mechanism selects a balanced–efficient matching that cannot be manipulated by students and it respects internal priority bylaws of colleges regarding dependent eligibility. Moreover, it makes full participation a dominant strategy for colleges, thus encouraging exchange. We also show that 2S-TTC is the unique optimal mechanism fulfilling these objectives. There also exist tuition co-ops where maintaining a one–to–one balance is not the first objective. For these programs, to minimize imbalance while respecting stability, we also propose a new flexible mechanism with desirable properties. JEL Classification Numbers: C71, C78, D71, D78 Keywords: Market Design, Matching Theory, Tuition Exchange, Balanced Exchange, Two–sided Match- ing, Two–sided Top Trading Cycles ∗ We thank John Duffy for initial discussions, Michael Grubb, Jacob Leshno, and Konrad Mierendorff for very useful com- ments. We also acknowledge various comments we got from the audience during presentations at Texas, Rice, Zurich, Queen’s Belfast, Microsoft Research at New England, Frontiers of Market Design’12, Spring Midwest Theory Conference’12, Stony Brook Game Theory Conference’12, Match-Up’12, Games’12, and Social Choice and Welfare’12 and thank them. † Address: The University of Texas at Austin, Department of Economics, 2225 Speedway, Austin, TX, 78712; e-mail: umut- dur@gmail.com; web page: https://sites.google.com/site/umutdur/ ‡ Address: Boston College, Department of Economics, 140 Commonwealth Ave., Chestnut Hill, MA, 02467; e-mail: un- ver@bc.edu; web page: http://www2.bc.edu/~unver 1