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Coalitional Stability and Incentives in Housing Markets with Incomplete Preferences

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  • Emilio Guaman
  • Juan Pablo Torres-Martinez

Abstract

We study the non-monetary exchange of indivisible goods when agents may not know how to compare some of them. Adding incomplete preferences to the Shapley-Scarf housing market model, we introduce two concepts of coalitional stability -the core and the strong core- that differ by the conditions required by a group of agents to block a housing allocation. The core is the set of allocations immune to blocking coalitions that improve the well-being of house-switching members, while the strong core is the set of allocations immune to blocking coalitions that may leave some members with a house incomparable to the original. We show that the core coincides with the set of allocations obtained by applying the Top Trading Cycles algorithm to the transitive completions of agents preferences. This result allows us to find a family of core-selecting and group strategy-proof mechanisms. Although the strong core may be an empty set, in the preference domain in which it is non-empty and the incompleteness of preferences is transitive, we show that there are strong-core-selecting and weakly group strategy-proof mechanisms. We also extend these results to housing allocation problems in which existing tenants and newcomers may coexist.

Suggested Citation

  • Emilio Guaman & Juan Pablo Torres-Martinez, 2023. "Coalitional Stability and Incentives in Housing Markets with Incomplete Preferences," Working Papers wp547, University of Chile, Department of Economics.
    • Handle: RePEc:udc:wpaper:wp547
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    References listed on IDEAS

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