A New Solvable Weak Priority Structure

Abstract

Organizations (especially firms) often rotate employees’ jobs from period to period. We propose a market design approach to organize job rotation in any given period. In our model each employee has occupied a position. Rotation requires that the occupier of a position must leave if any other employee wants to move to the position. This requirement is described by a priority structure in which each employee has the lowest priority for his occupied position and other employees have equal priority. Interestingly, this priority structure can be regarded as the “opposite” to the famous housing market priority structure (Shapley and Scarf, 1974). We adapt the Top Trading Cycle mechanism to solve the model. Our mechanism is innovative in that we preclude employees from pointing to their positions during the procedure of the mechanism and we do not clear cycles immediately when they appear; instead, after all employees are involved in cycles, we clear cycles by backward induction. Our mechanism is stable, constrained efficient and weakly group strategy-proof. Our mechanism (partially) answers an open question of Ehlers and Westkamp (2018) on the solvability of coarse priority structures.