Two-Sided Matching With Externalities: A Survey

Abstract

The literature on two-sided matching markets with externalities has grown over the past several years, as it is now one of the primary topics of research in two-sided matching theory. A matching market with externalities is different from the classical matching market in that agents not only care about who they are matched with, but also care about whom other agents are matched to. In this survey, we start with two-sided matching markets with externalities for the one-to-one case and then focus on the many-to-one case. For many-to-one matching problems, these externalities often are present in two ways. First, the agents on the "many" side may care about who their colleagues are, that is, who else is matched to the same "one." Second, the "one" side may care about how the others are matched.

Mergers and acquisitions matching for performance improvement: a DEA-based approach

“…TSM now has been broadly applied across a wide spectrum of socio-economic activities, such as electronic brokering (Jiang et al, 2011;Le et al, 2018), person-job fit (Azevedo, 2014;Lin et al, 2019a), venture capital matching (Sørensen, 2007), mergers and acquisitions (Akkus et al, 2016;Park, 2013;Wanke et al, 2019), etc. An introductory survey of TSM has been carried out by Roth and Sotomayor (1992); Bando et al (2016) also summarized some existing matching models with externalities.…”

Incentives and implementation in marriage markets with externalities

“…Dening stability in markets with externalities is not straightforward. Indeed, it has to take into account the expectations of a potential deviating agent or pair about the behavior of the other agents (see Bando and Muto, 2016). We consider a concept of stability based on prudent expectations.…”

Competitive equilibria in Shapley–Scarf markets with couples

“…shows that every non-competitive allocation is weakly dominated by some competitive allocation and the non-empty strict core is the unique von Neumann-Morgenstern solution.2 Further properties of Shapley-Scarf markets may be found inBird (1984),Sönmez (1996),Abdulkadiroğlu and Sönmez (1999), and Sönmez (1999).3 The reader may refer toRoth and Sotomayor (1990),Sasaki and Toda (1996),Dutta and Massó (1997),Roth and Peranson (1999),Cantala et al (2004),Klaus and Klijn (2005),Echenique and Yenmez (2007),Klaus et al (2007),Hafalir (2008),Mumcu and Saglam (2010), Bando (2012), Pycia (2012), Bando (2014),Pycia and Yenmez (2014),Fisher and Hafalir (2016). See alsoBando et al (2016) for a recent survey.4 InHong and Park (2018), each individual cares about others only when comparing allocations assigning her to the same good. They show that with this type of egocentric preferences, the properties of the TTC algorithm essentially remain satisfied.…”