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Balanced Exchange in a Multi-Unit Shapley-Scarf Market

Author

Listed:
  • Szilvia Pápai
  • Péter Biró
  • Flip Klijn

Abstract

We study markets in which each agent is endowed with multiple units of an indivisible and agent-specific good. Monetary compensations are not possible. An outcome of a market is given by a circulation which consists of a balanced exchange of goods. Agents only have (responsive) preferences over the bundles they receive. We prove that for general capacity configurations there is no circulation rule that satisfies individual rationality, Pareto-efficiency, and strategy-proofness. We characterize the (so-called irreducible) capacity configurations for which the three properties are compatible, and show that in this case the Circulation Top Trading Cycle (cTTC) rule is the unique rule that satisfies all three properties. We also explore the incentive and efficiency properties of the cTTC rule for general capacity configurations and provide a characterization of the rule for lexicographic preferences. Next, we introduce and study the family of so-called Segmented Trading Cycle (STC) rules. These rules are obtained by first distributing agents' endowments over a number of different smaller markets (the market segments), then applying the standard Top Trading Cycle algorithm within each market segment separately, and finally lumping together the induced circulations. We show that STC rules are individually rational, strategy-proof, and nonbossy. Even though STC rules do not satisfy group-strategy-proofness in general, they do satisfy weaker notions of group-strategy-proofness. For irreducible capacity configurations the family of STC rules collapses to the cTTC rule which then is also group-strategy-proof. Finally, we characterize one particularly interesting STC rule by means of top unanimity and self-enforcing group-strategy-proofness.

Suggested Citation

  • Szilvia Pápai & Péter Biró & Flip Klijn, 2022. "Balanced Exchange in a Multi-Unit Shapley-Scarf Market," Working Papers 1342, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1342
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    References listed on IDEAS

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    1. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
    2. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    3. 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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    Cited by:

    1. Gian Caspari, 2026. "Booster draft mechanisms for multi-object assignment," International Journal of Game Theory, Springer;Game Theory Society, vol. 55(1), pages 1-20, June.
    2. Feng, Di, 2025. "Efficiency in multiple-type housing markets," Journal of Mathematical Economics, Elsevier, vol. 119(C).
    3. Hosseinzadeh Ranjbar, Homa & Feizi, Mehdi, 2025. "Credibility of group manipulation in random assignments," Games and Economic Behavior, Elsevier, vol. 150(C), pages 27-33.

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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