Optimal truncation in matching markets

Abstract

Since no stable matching mechanism can induce truth-telling as a dominant strategy for all participants, there is often room in matching markets for strategic misrepresentation (Roth [25]). In this paper we study a natural form of strategic misrepresentation: reporting a truncation of one's true preference list. Roth and Rothblum [28] prove an important but abstract result: in certain symmetric, incomplete information settings, agents on one side of the market ("the women") optimally submit some truncation of their true preference lists. In this paper we put structure on this truncation, both in symmetric and general settings, when agents must submit preference lists to the Men-Proposing Deferred Acceptance Algorithm.We first characterize each woman's truncation payoffs in an incomplete information setting in terms of the distribution of her achievable mates. The optimal degree of truncation can be substantial: we prove that in a uniform setting, the optimal degree of truncation for an individual woman goes to 100% of her list as the market size grows large, when other women are truthful. In this setting, we demonstrate the existence of an equilibrium where all agents use truncation strategies. Compared to truthful reporting, in any equilibrium in truncation strategies, welfare diverges for men and women: women prefer the truncation equilibrium, while men would prefer that participants truthfully report.In a general environment, we show that the less risk averse a player, the greater the degree of her optimal truncation. Finally, when correlation in preferences increases, players should truncate less. While several recent papers have focused on the limits of strategic manipulation, our results serve as a reminder that without the pre-conditions ensuring truthful reporting, even in settings where agents have little information, the potential for manipulation can be significant.

Multi-Scenarios Dynamic Matching Algorithm for Hierarchical Treatment System

“…Ingolfsson (2010) proposed a vertical bilateral market matching price strategy, Feldman (2008) obtained the pricing model of the bilateral market matching when the participants were unequal [7]. In the specific application areas, bilateral market matching pricing decision research has also become a hot topic, as the e-commerce platform pricing [8], renewable energy power system pricing [9], self-media social platform Pricing [10], bilateral pricing model decision in media [11].…”

On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets

“…6 Kojima and Pathak (2009, Lemma 1) proved that the dropping correspondence is exhaustive for a firm in the many-to-one model (where workers' quotas equal one). 7 However, their result does not say anything about possible joint manipulations by a group of workers or a group of firms, nor deals with the possibility of workers having a quota larger than one. 8 We show that for each stable mechanism, the dropping correspondence is exhaustive for each group of agents on the same side of the market (Theorem 1).…”

“…Taking the stability requirement for a mechanism to perform well as granted, we study stable mechanisms, but do not restrict ourselves to the firm-optimal stable mechanism (as in Roth and Rothblum, 1999, and Coles and Shorrer, 2012). On the other hand, we assume a complete information environment.…”

“…We rephrase their Theorem 2 to fit it for our framework. 7 In fact, Kojima and Pathak (2009) also considered strategic manipulation by underreporting quotas. We focus on manipulation via preference lists, and aim to establish "exhaustiveness results" (of truncation and dropping strategies) for different classes of quota vectors.…”

“…Since ϕ(Q, q) ∈ S(Q, q), ϕ w (Q, q) R w f * = ϕ w (P * w , P −w , q). 22 Truncation strategies have been extensively studied in the matching literature (Roth and Vande Vate, 1991, Ehlers, 2008, Romm, 2011, Ashlagi and Klijn, 2012, Coles and Shorrer, 2012, among others). Moreover, they have been used in practice, for instance, in the sorority rush (Mongell and Roth, 1991).…”