On the Susceptibility of the Deferred Acceptance Algorithm

TL;DR

This paper investigates how the Deferred Acceptance Algorithm can be manipulated by agents with capacity, revealing that such manipulation is often computationally feasible and occurs frequently in two-sided matching markets.

Contribution

It introduces the first analysis of manipulation complexity for capacity-involving agents in DAA and provides efficient algorithms for such manipulations.

Findings

Manipulation is often possible with efficient algorithms.

Agents frequently have incentives to misreport preferences.

Manipulability occurs often in simulated matching markets.

Abstract

The Deferred Acceptance Algorithm (DAA) is the most widely accepted and used algorithm to match students, workers, or residents to colleges, firms or hospitals respectively. In this paper, we consider for the first time, the complexity of manipulating DAA by agents such as colleges that have capacity more than one. For such agents, truncation is not an exhaustive strategy. We present efficient algorithms to compute a manipulation for the colleges when the colleges are proposing or being proposed to. We then conduct detailed experiments on the frequency of manipulable instances in order to get better insight into strategic aspects of two-sided matching markets. Our results bear somewhat negative news: assuming that agents have information other agents' preference, they not only often have an incentive to misreport but there exist efficient algorithms to find such a misreport.