Dynamics, Stability, and Foresight in the Shapley-Scarf Housing Market
AbstractWhile 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.
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Bibliographic InfoPaper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2009.51.
Date of creation: Jun 2009
Date of revision:
Indivisible Goods Market; Dynamics; Competitive Allocation; Strict Core; Foresight; Stable Set;
Other versions of this item:
- Kamijo, Yoshio & Kawasaki, Ryo, 2010. "Dynamics, stability, and foresight in the Shapley-Scarf housing market," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 214-222, March.
- D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy-Making and Implementation
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-07-28 (All new papers)
- NEP-GTH-2009-07-28 (Game Theory)
- NEP-URE-2009-07-28 (Urban & Real Estate Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
- Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-80, November.
- 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.
- 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.
- 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.
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