“…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.…”