On Stable and Strategy-Proof Rules in Matching Markets with Contracts

Abstract

This paper studies stable and (one-sided) strategy-proof matching rules in manyto-one matching markets with contracts. First, the number of such rules is shown to be at most one. Second, the doctor-optimal stable rule, whenever it exists, is shown to be the unique candidate for a stable and strategy-proof rule. Third, a stable and strategyproof rule, when exists, is shown to be second-best optimal for doctor welfare, in the sense that no individually-rational and strategy-proof rule can dominate it. This last result is further generalized to non-wasteful and strategy-proof rules. Notably, all those results are established without any substitutes conditions on hospitals' choice functions, and hence, the proofs do not rely on the "rural hospital" theorem. We also show by example that the outcomes of a stable and strategy-proof rule do not always coincide with those of the cumulative offer process; hence, the above results hold not because the cumulative offer process is the only candidate for stable and strategyproof rules.

School choice with preference rank classes

“…We also prove that the only strategyproof PRP rule is the Deferred Acceptance rule (Theorem 3). Hirata and Kasuya (2017) study stability and strategyproofness in a general matching market with contracts, and find that the number of stable and strategy-proof rules is at most one. They also show that if the student-optimal stable rule exists then it is the only candidate for a stable and strategyproof rule.…”