Two-sided strategy-proofness in many-to-many matching markets

Abstract

We study the existence of group strategy-proof stable rules in many-to-many matching markets under responsiveness of agents’ preferences. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proof rule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof mechanisms in many-to-many matching markets.

Centralized Course Allocation

“…Under essential homogeneity, the mechanism required to implement stable allocations is equivalent to a serial dictatorship in which the order of choice depends on the distribution of seats among courses. If we require the mechanism to be independent of the seat distribution, a stable mechanism that makes true preferences a dominant strategy exists if and only if priorities are acyclical (see Romero-Medina and Triossi, 2018). Essential homogeneity and acyclicity impose severe restrictions on the design of priorities.…”