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Community Costs in Neighborhood Help Problems

Author

Listed:
  • Sarah Kühn

    (Paderborn University)

  • Nadja Stroh-Maraun

    (Paderborn University)

Abstract

We define neighborhood help problems where agents may seek and/or provide various kinds of help as matching markets with an explicitly modeled outside option. In most matching markets a short supply of compatible helpers may result in many agents being unmatched, forcing them to rely on costly outside options. These unmatched agents leave the market without helping and substantial potential is lost. To overcome this issue we introduce the pool option which incentivizes agents to provide help while receiving help outside the market. By explicitly modeling the outside option our model becomes applicable to a broad range of applications. The top trading cycles (TTC) mechanism (Shapley & Scarf, 1974) no longer provides a Pareto efficient allocation in this setting. Thus, we propose the neighborhood top trading cycles and chains (NTTCC) mechanism which incorporates the pool option and is based on the TTCC by Roth et al. (2004). The NTTCC is individual rational, Pareto efficient, and strategy-proof. The NTTCC (weakly) reduces overall costs compared to the TTC. More generally, the NTTCC is cost-minimal in the class of individual rational and Pareto-efficient mechanisms.

Suggested Citation

  • Sarah Kühn & Nadja Stroh-Maraun, 2025. "Community Costs in Neighborhood Help Problems," Working Papers CIE 167, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:167
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    References listed on IDEAS

    as
    1. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    2. Stroh-Maraun, Nadja, 2024. "Weighted school choice problems and the weighted top trading cycles mechanism," Mathematical Social Sciences, Elsevier, vol. 132(C), pages 49-56.
    3. Zenios, Stefanos & Woodle, E. Steve & Ross, Lainie Friedman, 2001. "Primum Non Nocere: Avoiding Harm to Vulnerable Wait List Candidates in an Indirect Kidney Exchange," Research Papers 1684, Stanford University, Graduate School of Business.
    4. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    5. Sonmez, Tayfun & Utku Unver, M., 2005. "House allocation with existing tenants: an equivalence," Games and Economic Behavior, Elsevier, vol. 52(1), pages 153-185, July.
    6. Yu Wang & Aradhna Krishna, 2006. "Timeshare Exchange Mechanisms," Management Science, INFORMS, vol. 52(8), pages 1223-1237, August.
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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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