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Dynamics, Stability, and Foresight in the Shapley-Scarf Housing Market


  • Yoshio Kamijo

    (Waseda University)

  • Ryo Kawasaki

    (Tokyo Institute of Technology)


While most of the literature starting with Shapley and Scarf (1974) have considered a static exchange economy with indivisibilities, this paper studies the dynamics of such an economy. We find that both the dynamics generated by competitive equilibrium and the one generated by weakly dominance relation, converge to a set of allocations we define as strictly stable, which we can show to exist. Moreover, we show that even when only pairwise exchanges between two traders are allowed, the strictly stable allocations are attained eventually if traders are sufficiently farsighted.

Suggested Citation

  • Yoshio Kamijo & Ryo Kawasaki, 2009. "Dynamics, Stability, and Foresight in the Shapley-Scarf Housing Market," Working Papers 2009.51, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2009.51

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    References listed on IDEAS

    1. Sotomayor, Marilda, 2005. "An elementary non-constructive proof of the non-emptiness of the core of the Housing Market of Shapley and Scarf," Mathematical Social Sciences, Elsevier, vol. 50(3), pages 298-303, November.
    2. Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
    5. 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.
    6. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    7. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    8. Wako, Jun, 1984. "A note on the strong core of a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 189-194, October.
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    Cited by:

    1. Morimitsu Kurino, 2014. "House Allocation with Overlapping Generations," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 258-289, February.
    2. Kawasaki, Ryo, 2015. "Roth–Postlewaite stability and von Neumann–Morgenstern stability," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 1-6.

    More about this item


    Indivisible Goods Market; Dynamics; Competitive Allocation; Strict Core; Foresight; Stable Set;

    JEL classification:

    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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