On the Susceptibility of the Deferred Acceptance Algorithm

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.

Manipulating the outcome of stable matching and roommates problems

“…Hosseini et al [17] investigated cases where the coalition can contain both men and women. Aziz et al [3] investigated the case where the agents who want to manipulate the outcome have capacity larger than one, like firms or hospitals. Coalitional manipulations where a fixed subset of edges must be contained in the output of the Gale-Shapley algorithm has been studied by Kobayashi and Matsui [20] and by Gupta and Roy [15].…”