Strategyproof Matching of Roommates and Rooms

TL;DR

This paper studies a matching problem where agents with Leontief utilities are assigned to rooms, balancing social welfare maximization and strategyproofness, and finds new mechanisms that achieve both under certain conditions.

Contribution

It introduces strategyproof mechanisms for roommate-room matching with Leontief utilities that maximize social welfare, contrasting with the additive case.

Findings

Existence of strategyproof, welfare-maximizing mechanisms under binary Leontief utilities.

A parameterized strategyproof mechanism based on the number of agents.

Impossibility results and bounds for welfare with/without strategyproofness.

Abstract

We initiate the study of matching roommates and rooms wherein the preferences of agents over other agents and rooms are complementary and represented by Leontief utilities. In this setting, 2n agents must be paired up and assigned to n rooms. Each agent has cardinal valuations over the rooms as well as compatibility values over all other agents. Under Leontief preferences, an agents utility for a matching is the minimum of the two values. We focus on the tradeoff between maximizing utilitarian social welfare and strategyproofness. Our main result shows that, in a stark contrast to the additive case, under binary Leontief utilities, there exist strategyproof mechanisms that maximize the social welfare. We further devise a strategyproof mechanism that implements such a welfare maximizing algorithm and is parameterized by the number of agents. Along the way, we highlight several possibility and impossibility results, and give upper bounds and lower bounds for welfare with or without strategyproofness.