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On the Shapley-Scarf economy: the case of multiple types of indivisible goods

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  • Konishi, Hideo
  • Quint, Thomas
  • Wako, Jun

Abstract

We study a generalization of Shapley-Scarf's (1974) economy in which multiple types of indivisible goods are traded. We show that many of the distinctive results from the Shapley-Scarf economy do not carry over to this model, even if agents' preferences are strict and can be represented by additively separable utility functions. The core may be empty. The strict core, if nonempty, may be multi-valued, and might not coincide with the set of competitive allocations. Furthermore, there is no Pareto efficient, individually rational, and strategy-proof social choice rule. We also show that the core may be empty in the class of economies with a single type of indivisible good and agents consuming multiple units, even if no complementarity exists among the goods.

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Bibliographic Info

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

Volume (Year): 35 (2001)
Issue (Month): 1 (February)
Pages: 1-15

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Handle: RePEc:eee:mateco:v:35:y:2001:i:1:p:1-15

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

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  1. Sonmez, T., 1995. "Implementation in Generalized Matching Problems," Papers 95-03, Michigan - Center for Research on Economic & Social Theory.
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Cited by:
  1. Inoue, Tomoki, 2008. "Indivisible commodities and the nonemptiness of the weak core," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 96-111, January.
  2. Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.
  3. Dimitrov,Dinko & Haake,Claus-Jochen & Klaus,Bettina, 2005. "Bundling in Exchange Markets with Indivisible Goods," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Vendrik, Maarten & Woltjer, Geert, 2006. "Happiness and Loss Aversion: When Social Participation Dominates Comparision," Research Memorandum 027, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Budish, Eric & Cantillon, Estelle, 2010. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," CEPR Discussion Papers 7641, C.E.P.R. Discussion Papers.
  6. Dinko Dimitrov & Claus-Jochen Haake, 2005. "Regrouping of endowments in exchange markets with indivisible goods," Working Papers 367, Bielefeld University, Center for Mathematical Economics.

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