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Serial Rules in a Multi-Unit Shapley-Scarf Market

Author

Listed:
  • Szilvia Pápai
  • Péter Biró
  • Flip Klijn

Abstract

We study generalized Shapley-Scarf exchange markets where each agent is endowed with multiple units of an indivisible and agent-specific good and monetary compensations are not possible. An outcome is given by a circulation which consists of a balanced exchange of goods. We focus on circulation rules that only require as input ordinal preference rankings of individual goods, and agents are assumed to have responsive preferences over bundles of goods. We study the properties of serial dictatorship rules which allow agents to choose either a single good or an entire bundle sequentially, according to a fixed ordering of the agents. We also introduce and explore extensions of these serial dictatorship rules that ensure individual rationality. The paper analyzes the normative and incentive properties of these four families of serial dictatorships and also shows that the individually rational extensions can be implemented with efficient graph algorithms.

Suggested Citation

  • Szilvia Pápai & Péter Biró & Flip Klijn, 2021. "Serial Rules in a Multi-Unit Shapley-Scarf Market," Working Papers 1255, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1255
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    Cited by:

    1. Han, Xiang, 2024. "A theory of fair random allocation under priorities," Theoretical Economics, Econometric Society, vol. 19(3), July.
    2. Feng, Di & Klaus, Bettina & Klijn, Flip, 2024. "Characterizing the typewise top-trading-cycles mechanism for multiple-type housing markets," Games and Economic Behavior, Elsevier, vol. 146(C), pages 234-254.
    3. Echenique, Federico & Goel, Sumit & Lee, SangMok, 2024. "Stable allocations in discrete exchange economies," Journal of Economic Theory, Elsevier, vol. 222(C).
    4. Péter Biró & Sándor Bozóki & Tamás Király & Alexandru Kristály, 2024. "Optimization methods and algorithms," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(1), pages 1-9, March.
    5. Mih'aly P'eter Hanics, 2022. "Graph theoretical models and algorithms of portfolio compression," Papers 2212.09473, arXiv.org.

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    More about this item

    Keywords

    efficiency; indivisible goods; circulation; Shapley-Scarf market; serial dictatorship;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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