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Matching with externalities: The role of prudence and social connectedness in stability

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  • Braitt, Milton dos Santos
  • Torres-Martínez, Juan Pablo

Abstract

In matching problems with externalities, prudence measures the importance an agent gives to others’ potential reactions when she considers deviating and social connectedness measures others’ capacity to react to the agent’s deviation. Assuming that externalities and preferences are random, the roles of prudence and social connectedness are studied. It is shown that asymptotic stability – a property that never holds in the absence of externalities – is achieved when the product of social connectedness and prudence grows at least exponentially with the population. Since social connectedness increases quickly in both the marriage and roommates markets, stability obtains even when prudence vanishes (sufficiently slowly).

Suggested Citation

  • Braitt, Milton dos Santos & Torres-Martínez, Juan Pablo, 2021. "Matching with externalities: The role of prudence and social connectedness in stability," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 95-102.
    • Handle: RePEc:eee:mateco:v:92:y:2021:i:c:p:95-102
    DOI: 10.1016/j.jmateco.2020.09.003
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    References listed on IDEAS

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    1. Sasaki, Hiroo & Toda, Manabu, 1996. "Two-Sided Matching Problems with Externalities," Journal of Economic Theory, Elsevier, vol. 70(1), pages 93-108, July.
    2. Fisher, James C.D. & Hafalir, Isa E., 2016. "Matching with aggregate externalities," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 1-7.
    3. Boris Pittel, 2019. "On random stable partitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 433-480, June.
    4. Bando, Keisuke, 2012. "Many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 14-20.
    5. Mumcu, Ayse & Saglam, Ismail, 2010. "Stable one-to-one matchings with externalities," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 154-159, September.
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