Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2021 Oct;23(5):822-857.
doi: 10.1111/jpet.12542. Epub 2021 Sep 15.

Matching Soulmates

Greg Leo  1 , Jian Lou  2 , Martin Van der Linden  3 , Yevgeniy Vorobeychik  4 , Myrna Wooders  1
Affiliations

Matching Soulmates

Greg Leo et al. J Public Econ Theory. 2021 Oct.

Abstract

We study iterated matching of soulmates [IMS], a recursive process of forming coalitions that are mutually preferred by members to any other coalition containing individuals as yet unmatched by this process. If all players can be matched this way, preferences are IMS-complete. A mechanism is a soulmate mechanism if it allows the formation of all soulmate coalitions. Our model follows Banerjee, Konishi and Sönmez (2001), except reported preferences are strategic variables. We investigate the incentive and stability properties of soulmate mechanisms. In contrast to prior literature, we do not impose conditions that ensure IMS-completeness. A fundamental result is that, (1) any group of players who could change their reported preferences and mutually benefit does not contain any players who were matched as soulmates and reported their preferences truthfully. As corollaries, (2) for any IMS-complete profile, soulmate mechanisms have a truthful strong Nash equilibrium, and (3) as long as all players matched as soulmates report their preferences truthfully, there is no incentive for any to deviate. Moreover, (4) soulmate coalitions are invariant core coalitions - that is, any soulmate coalition will be a coalition in every outcome in the core. To accompany our theoretical results, we present real-world data analysis and simulations that highlight the prevalence of situations in which many, but not all, players can be matched as soulmates. In an Appendix we relate IMS to other well-known coalition formation processes.

PubMed Disclaimer

Figures

Figure 1:
Figure 1:
Venn diagram of the profile conditions. A dot indicates that the section of the Venn diagram is non-empty. The inclusion relationship is trivial. For examples of profiles of type A see Banerjee, Konishi and Sönmez (2001, Section 6). For an example of a profile of type B, see Banerjee, Konishi and Sönmez (2001, Game 4). Example 1 in this paper is a profile of type C. Example 5 in this paper is a profile of type D (any other profile for which the core is empty would also be an example).
Figure 2:
Figure 2:
Proportion of Players Matched and IMS-Complete Profiles by Level of Commonality (D) for N = 10
Figure 3:
Figure 3:
Proportion of Players Matched and IMS-Complete Profiles for by Level of Commonality (D) for N = 10
See this image and copyright information in PMC

References

    1. Abdulkadiroğlu Atila, and Tayfun Sönmez. 2003. “School choice: a mechanism design approach.” The American Economic Review, 93(3): 729–747.
    1. Alcalde José, and Antonio Romero-Medina. 2006. “Coalition formation and stability.” Social Choice and Welfare, 27(2): 365–375.
    1. Aumann Robert J. 1959. “Acceptable points in general cooperative n-person games.” Contributions to the Theory of Games, 4: 287–324.
    1. Banerjee Suryapratim, Konishi Hideo, and Sönmez Tayfun. 2001. “Core in a simple coalition formation game.” Social Choice and Welfare, 18(1): 135–153.
    1. Basteck Christian, and Mantovani Marco. 2016a. “Cognitive Ability and Games of School Choice.” University of Milan Bicocca Department of Economics, Management and Statistics Working Paper, , (343).

LinkOut - more resources