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A Characterization of the Coordinate-Wise Top-Trading-Cycles Mechanism for Multiple-Type Housing Markets

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  • Di Feng
  • Bettina Klaus
  • Flip Klijn

Abstract

We consider the generalization of the classical Shapley and Scarf housing market model of trading indivisible objects (houses) (Shapley and Scarf, 1974) to so-called multiple-type housing markets (Moulin, 1995). When preferences are separable, the prominent solution for these markets is the coordinate-wise top-trading-cycles (cTTC) mechanism. We first show that on the subdomain of lexicographic preferences, a mechanism is unanimous (or onto), individually rational, strategy-proof, and non-bossy if and only if it is the cTTC mechanism (Theorem 1). Second, using Theorem 1, we obtain a corresponding characterization on the domain of separable preferences (Theorem 2). Finally, we show that on the domain of strict preferences, there is no mechanism satisfying unanimity (or ontoness), individual rationality, strategy-proofness, and non-bossiness (Theorem 3).Our characterization of the cTTC mechanism constitutes the first characterization of an extension of the prominent top-trading-cycles (TTC) mechanism to multiple-type housing markets.

Suggested Citation

  • Di Feng & Bettina Klaus & Flip Klijn, 2022. "A Characterization of the Coordinate-Wise Top-Trading-Cycles Mechanism for Multiple-Type Housing Markets," Cahiers de Recherches Economiques du Département d'économie 22.06, Université de Lausanne, Faculté des HEC, Département d’économie.
    • Handle: RePEc:lau:crdeep:22.06
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    References listed on IDEAS

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    1. Monte, Daniel & Tumennasan, Norovsambuu, 2015. "Centralized allocation in multiple markets," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 74-85.
    2. Bird, Charles G., 1984. "Group incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 14(4), pages 309-313.
    3. Manjunath, Vikram & Westkamp, Alexander, 2021. "Strategy-proof exchange under trichotomous preferences," Journal of Economic Theory, Elsevier, vol. 193(C).
    4. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    5. Klaus, Bettina, 2008. "The coordinate-wise core for multiple-type housing markets is second-best incentive compatible," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 919-924, September.
    6. Konishi, Hideo & Quint, Thomas & Wako, Jun, 2001. "On the Shapley-Scarf economy: the case of multiple types of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 1-15, February.
    7. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    8. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
    9. Takamiya, Koji, 2001. "Coalition strategy-proofness and monotonicity in Shapley-Scarf housing markets," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 201-213, March.
    10. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    11. Wako, Jun, 2005. "Coalition-proof Nash allocation in a barter game with multiple indivisible goods," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 179-199, March.
    12. Di Feng & Bettina Klaus, 2022. "Preference revelation games and strict cores of multiple‐type housing market problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 61-76, March.
    13. Miyagawa, Eiichi, 2002. "Strategy-Proofness and the Core in House Allocation Problems," Games and Economic Behavior, Elsevier, vol. 38(2), pages 347-361, February.
    14. Woonghee Tim Huh & Nan Liu & Van-Anh Truong, 2013. "Multiresource Allocation Scheduling in Dynamic Environments," Manufacturing & Service Operations Management, INFORMS, vol. 15(2), pages 280-291, May.
    15. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
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    More about this item

    Keywords

    : multiple-type housing markets; strategy-proofness; non-bossiness; top-trading-cycles (TTC) mechanism; market design;
    All these keywords.

    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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