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Dynamics, stability, and foresight in the Shapley-Scarf housing market

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  • Kamijo, Yoshio
  • Kawasaki, Ryo

Abstract

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 the weak 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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 2 (March)
Pages: 214-222

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Handle: RePEc:eee:mateco:v:46:y:2010:i:2:p:214-222

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Indivisible goods market Dynamics Competitive allocation Strict core Foresight Stable set;

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  1. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, Elsevier, vol. 48(1), pages 18-28, July.
  2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 1(1), pages 23-37, March.
  3. Wako, Jun, 1984. "A note on the strong core of a market with indivisible goods," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 13(2), pages 189-194, October.
  4. Roberto Serrano & Oscar Volij, 2003. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economics Working Papers, Institute for Advanced Study, School of Social Science 0029, Institute for Advanced Study, School of Social Science.
  5. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, 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, 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, Econometric Society, vol. 58(6), pages 1475-80, November.
  8. 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, Elsevier, vol. 50(3), pages 298-303, November.
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Cited by:
  1. Morimitsu Kurino, 2014. "House Allocation with Overlapping Generations," American Economic Journal: Microeconomics, American Economic Association, American Economic Association, vol. 6(1), pages 258-89, February.

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