Matching with slot-specific priorities: Theory

Abstract

We introduce a two-sided, many-to-one matching with contracts model in which agents with unit demand match to branches that may have multiple slots avail- able to accept contracts. Each slot has its own linear priority order over contracts; a branch chooses contracts by filling its slots sequentially, according to an order of precedence. We demonstrate that in these matching markets with slot-specific priorities, branches’ choice functions may not satisfy the substitutability condi- tions typically crucial for matching with contracts. Despite this complication, we are able to show that stable outcomes exist in the slot-specific priorities frame- work and can be found by a cumulative offer mechanism that is strategy-proof and respects unambiguous improvements in priority.