Abstract
Top Trading Cycles was originally developed as an elegant method for finding a competitive equilibrium of Shapley and Scarf's housing market. We extend the definition of a competitive equilibrium to the school assignment problem and show that there remains a profound relationship between Top Trading Cycles and a competitive equilibrium. Specifically, in every competitive equilibrium with weakly decreasing prices, the equilibrium assignment is unique and exactly corresponds to the Top Trading Cycles assignment. This provides a new way of interpreting the worth of a student's priority at a given school. It also provides a new way of explaining Top Trading Cycles to students and a school board.
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