A Weakly Group Strategy-Proof and Pareto-Stable Matching Mechanism with Two-Sided Indifferences under Gross Substitutes

Abstract

We study finite many-to-one matching markets with indifferences on both sides and publicly known firm preferences over sets of workers. A standard approach breaks ties uniformly at random and runs deferred acceptance, which is strategy-proof for workers but may select a weakly stable matching that is Pareto dominated under the agents' original preferences. For the broad class of markets in which each firm's preferences admit a gross substitutes (GS) representation, we construct a deterministic generalized deferred acceptance mechanism that is weakly stable, Pareto efficient with respect to both sides, worker weakly group strategy-proof, and implementable in strongly polynomial time given value oracles for the GS representations. This domain includes nonresponsive firm preferences, such as additive scores under matroid constraints and assignment values. Our analysis bridges ordinal matching with indifferences and competitive equilibria under imperfectly transferable utility. Although the mechanism uses only ordinal comparisons, it returns a seller-optimal equilibrium matching of a tiered auxiliary market, and the equilibrium structure of this market yields the stability, efficiency, and incentive guarantees.