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Random assignments on sequentially dichotomous domains

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  • Liu, Peng

Abstract

We present a possibility result on the existence of a random assignment rule satisfying sd-strategy-proofness, sd-efficiency, and equal treatment of equals. In particular, we introduce a class of preference domains: sequentially dichotomous domains. On any such domain, the probabilistic serial rule (Bogomolnaia and Moulin (2001)) is sd-strategy-proof. Moreover, any sequentially dichotomous domain is maximal for this rule to be sd-strategy-proof.

Suggested Citation

  • Liu, Peng, 2020. "Random assignments on sequentially dichotomous domains," Games and Economic Behavior, Elsevier, vol. 121(C), pages 565-584.
    • Handle: RePEc:eee:gamebe:v:121:y:2020:i:c:p:565-584
    DOI: 10.1016/j.geb.2019.05.006
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    References listed on IDEAS

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    1. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
    2. Bernard Monjardet, 2009. "Acyclic Domains of Linear Orders: A Survey," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 139-160, Springer.
    3. Mandler, Michael & Manzini, Paola & Mariotti, Marco, 2012. "A million answers to twenty questions: Choosing by checklist," Journal of Economic Theory, Elsevier, vol. 147(1), pages 71-92.
    4. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    5. Peter C. Fishburn, 2002. "Acyclic sets of linear orders: A progress report," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 431-447.
    6. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    7. 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.
    8. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    9. Chang, Hee-In & Chun, Youngsub, 2017. "Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 80-92.
    10. ,, 2009. "Asymptotic ordinal inefficiency of random serial dictatorship," Theoretical Economics, Econometric Society, vol. 4(2), June.
    11. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
    12. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    13. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    14. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    15. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    16. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 203-215, June.
    17. 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.
    18. Florian Brandl & Felix Brandt & Hans Georg Seedig, 2016. "Consistent Probabilistic Social Choice," Econometrica, Econometric Society, vol. 84, pages 1839-1880, September.
    19. Mihai Manea, 2008. "Random serial dictatorship and ordinally efficient contracts," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 489-496, March.
    20. P. C. Fishburn, 1984. "Probabilistic Social Choice Based on Simple Voting Comparisons," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(4), pages 683-692.
    21. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2209-2226, September.
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    Cited by:

    1. Sulagna Dasgupta & Debasis Mishra, 2022. "Ordinal Bayesian incentive compatibility in random assignment model," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 651-664, December.

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    More about this item

    Keywords

    Random assignment; Probabilistic serial rule; Sequentially dichotomous domain; Sd-strategy-proof;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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