# Investigating the Characteristics of One-Sided Matching Mechanisms Under Various Preferences and Risk Attitudes

## TL;DR

This paper compares two key one-sided matching mechanisms, RSD and PS, analyzing their economic properties, manipulability, and efficiency under various preferences and risk attitudes to guide practical adoption.

## Contribution

It provides empirical and theoretical insights into the comparability, economic properties, and robustness of RSD and PS across diverse preference and risk models.

## Key findings

- RSD is broadly applicable across different preference distributions.
- Mechanisms show varying levels of manipulability and envyfreeness.
- Outcomes of RSD and PS are often incomparable, complicating mechanism choice.

## Abstract

One-sided matching mechanisms are fundamental for assigning a set of indivisible objects to a set of self-interested agents when monetary transfers are not allowed. Two widely-studied randomized mechanisms in multiagent settings are the Random Serial Dictatorship (RSD) and the Probabilistic Serial Rule (PS). Both mechanisms require only that agents specify ordinal preferences and have a number of desirable economic and computational properties. However, the induced outcomes of the mechanisms are often incomparable and thus there are challenges when it comes to deciding which mechanism to adopt in practice. In this paper, we first consider the space of general ordinal preferences and provide empirical results on the (in)comparability of RSD and PS. We analyze their respective economic properties under general and lexicographic preferences. We then instantiate utility functions with the goal of gaining insights on the manipulability, efficiency, and envyfreeness of the mechanisms under different risk-attitude models. Our results hold under various preference distribution models, which further confirm the broad use of RSD in most practical applications.