Strategyproof Maximum Matching under Dichotomous Agent Preferences
Haris Aziz, Md. Shahidul Islam, Szilvia Pápai
TL;DR
The paper addresses matching with dichotomous agent preferences and strict institutional priorities, aiming to maximize acceptably matched agents while ensuring fairness and incentive compatibility. It introduces two equivalent mechanism families, SAFE and Rank-Maximal, based on safe blocks and lexicographic rank-maximality, respectively. These mechanisms achieve maximum-size matchings, fairness, and strategyproofness on both sides, plus non-bossiness and polynomial-time computability, answering a long-standing open question. The results have practical impact for centralized allocation problems such as daycare, schools, and healthcare resource distribution, offering robust, incentive-friendly allocations under capacity constraints.
Abstract
We consider a two-sided matching problem in which the agents on one side have dichotomous preferences and the other side representing institutions has strict preferences (priorities). It captures several important applications in matching market design in which the agents are only interested in getting matched to an acceptable institution. These include centralized daycare assignment and healthcare rationing. We present a compelling new mechanism that satisfies many prominent and desirable properties including individual rationality, maximum size, fairness, Pareto-efficiency on both sides, strategyproofness on both sides, non-bossiness and having polynomial time running time. As a result, we answer an open problem whether there exists a mechanism that is agent-strategyproof, maximum, fair and non-bossy.