Cheating by Men in the Gale-Shapley Stable Matching Algorithm

Abstract

Abstract. This paper addresses strategies for the stable marriage problem. For the Gale-Shapley algorithm with men proposing, a classical theorem states that it is impossible for every cheating man to get a better partner than the one he gets if everyone is truthful. We study how to circumvent this theorem and incite men to cheat. First we devise coalitions in which a non-empty subset of the liars get better partners and no man is worse off than before. This strategy is limited in that not everyone in the coalition has the incentive to falsify his list. In an attempt to rectify this situation we introduce the element of randomness, but the theorem shows surprising robustness: it is impossible that every liar has a chance to improve the rank of his partner while no one gets hurt. To overcome the problem that some men lack the motivation to lie, we exhibit another randomized lying strategy in which every liar can expect to get a better partner on average, though with a chance of getting a worse one. Finally, we consider a variant scenario: instead of using the Gale-Shapley algorithm, suppose the stable matching is chosen at random. We present a modified form of the coalition strategy ensuring that every man in the coalition has a new probability distribution over partners which majorizes the original one.

Cheating in matching of device to device pairs in cellular networks

“…A conclusion from [11] shows that CS is the only strategy that has the nice property of ensuring that some men are better off and every liar is at least as well off as before. This property is validated throughput our simulation results.…”

“…We let M 0 be the man-optimal stable matching. Different from Theorem 2 in [11], which doesn't specify how those unmatched users should perform, we define the actions for unmatched users, and find that, for the users within the cabal who affect other cabal members, their falsify strategy should be different from those outside the cabal. Thus, in this paper, we update Theorem 2 in [11], which is presented in Algorithm 2.…”

“…This so called "cheating/lying" action can be permutating some entries or truncating the lists, typically. In [11], Huang proposed a coalition strategy to let some men to be better off.…”

“…After matching, some D2D users may want to match to a better partner than the current match. Similar to the "cheating by men in the stable marriage" problem [11], the so called "coalition strategy (CS)" is applied to improve some unsatisfied D2D users' performance by falsifying certain users' preference lists. We illustrate how the CS algorithm can improve both D2D users' satisfaction.…”

Cooperative Game-based Cheating in Full-duplex Relaying-based D2D Communication Underlaying Heterogeneous Cellular Networks

“…Before plunging into technical details, we present a Theorem and two definitions about Cheating algorithm and give a proof of them based on [17], which presented the Cheating algorithm for the first time.…”