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Trading probabilities along cycles

Author

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  • Altuntaş, Açelya
  • Phan, William

Abstract

Consider the problem of allocating indivisible objects when agents are endowed with fractional amounts and rules can assign lotteries. We study a natural generalization (to the probabilistic domain) of Gale’s Top Trading Cycles. The latter features an algorithm wherein agents trade objects along a cycle—in our new family of rules, agents now trade probabilities of objects along a cycle. We ask if the attractive properties, namely efficiency, individual rationality, and strategy-proofness extended in the stochastic dominance sense, carry over to the Trading-Probabilities-Along-Cycles (TPAC) rules. All of these rules are sd-efficient. We characterize separately the subclass of TPAC rules satisfying the sd-endowment lower bound and sd-strategy-proofness. Regarding fairness, we follow in spirit to the no-envy in net trade condition of Schmeidler and Vind (1972), where the set of allocations satisfying the property essentially coincides with the set of competitive equilibria, and augment the notion appropriately for our environment. We further generalize the TPAC family while extending results on sd-efficiency and the sd-endowment lower bound, and provide sufficient conditions on parameters for the rules to arbitrarily closely satisfy the sd-no-envy in net trade.

Suggested Citation

  • Altuntaş, Açelya & Phan, William, 2022. "Trading probabilities along cycles," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    • Handle: RePEc:eee:mateco:v:100:y:2022:i:c:s0304406821001749
    DOI: 10.1016/j.jmateco.2021.102631
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    References listed on IDEAS

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    1. Stergios Athanassoglou & Jay Sethuraman, 2011. "House allocation with fractional endowments," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 481-513, August.
    2. YIlmaz, Özgür, 2010. "The probabilistic serial mechanism with private endowments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 475-491, July.
    3. Thayer Morrill, 2013. "An alternative characterization of top trading cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 181-197, September.
    4. Echenique, Federico & Miralles, Antonio & Zhang, Jun, 2021. "Fairness and efficiency for allocations with participation constraints," Journal of Economic Theory, Elsevier, vol. 195(C).
    5. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    6. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
    7. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    8. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    9. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    10. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August.
    11. Sophie Bade, 2020. "Random Serial Dictatorship: The One and Only," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 353-368, February.
    12. Morrill, Thayer, 2015. "Making just school assignments," Games and Economic Behavior, Elsevier, vol. 92(C), pages 18-27.
    13. Anno, Hidekazu, 2015. "A short proof for the characterization of the core in housing markets," Economics Letters, Elsevier, vol. 126(C), pages 66-67.
    14. Carroll, Gabriel, 2014. "A general equivalence theorem for allocation of indivisible objects," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 163-177.
    15. Thayer Morrill, 2015. "Two simple variations of top trading cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 123-140, September.
    16. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
    17. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2209-2226, September.
    18. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading algorithms in market design environments," Papers 2005.06878, arXiv.org, revised May 2021.
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    More about this item

    Keywords

    Top trading cycles; Probabilistic assignment; Efficiency; Strategy-proofness; Individual rationality; No-envy in net trade;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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