Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
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.