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Strategy-Proof Stochastic Assignment

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  • Aytek Erdil

Abstract

I study strategy-proof assignment mechanisms where the agents reveal their preference rankings over the available objects. A stochastic mechanism returns lotteries over deterministic assignments, and mechanisms are compared according to first-order stochastic dominance. I show that non-wasteful strategy-proof mechanisms are not dominated by strategy-proof mechanisms, however nonwastefulness is highly restrictive when the mechanism involves randomization. In fact, the Random Priority mechanism (i.e., the Random Serial Dictatorship), and a recently adopted school choice mechanism, Deferred Acceptance with Random Tie-breaking, are wasteful. I find that both these mechanisms are dominated by strategy-proof mechanisms. In general, strategy-proof improvement cannot be due to merely reshuffling objects, and therefore must involve assigning more objects. Forthcoming in

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  • Aytek Erdil, 2013. "Strategy-Proof Stochastic Assignment," Cambridge Working Papers in Economics 1333, Faculty of Economics, University of Cambridge.
  • Handle: RePEc:cam:camdae:1333
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    1. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    2. EHLERS, Lars, 2006. "Respecting Priorities when Assigning Students to Schools," Cahiers de recherche 04-2006, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. 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.
    4. Pathak, Parag A. & Sethuraman, Jay, 2011. "Lotteries in student assignment: An equivalence result," Theoretical Economics, Econometric Society, vol. 6(1), January.
    5. 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.
    6. Peters, Hans & Roy, Souvik & Sen, Arunava & Storcken, Ton, 2014. "Probabilistic strategy-proof rules over single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 123-127.
    7. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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    Cited by:

    1. Lars EHLERS & Dipjyoti MAJUMDAR & Debasis MISHRA & Arunava SEN, 2016. "Continuity and Incentive Compatibility in Cardinal Voting Mechanisms," Cahiers de recherche 04-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. André Schmelzer, 2017. "Strategy-proofness of stochastic assignment mechanisms," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2017_13, Max Planck Institute for Research on Collective Goods.
    3. Kesten, Onur & Kurino, Morimitsu & Nesterov, Alexander, 2015. "Efficient lottery design," Discussion Papers, Research Unit: Market Behavior SP II 2015-203, Social Science Research Center Berlin (WZB).
    4. Alexander Nesterov, 2014. "Fairness and Efficiency in a Random Assignment: Three Impossibility Results," Working Papers 2014006, Berlin Doctoral Program in Economics and Management Science (BDPEMS).
    5. Kesten, Onur & Kurino, Morimitsu, 2012. "On the (im)possibility of improving upon the student-proposing deferred acceptance mechanism," Discussion Papers, Research Unit: Market Behavior SP II 2012-202, Social Science Research Center Berlin (WZB).
    6. Hirata, Daisuke & Kasuya, Yusuke, 2017. "On stable and strategy-proof rules in matching markets with contracts," Journal of Economic Theory, Elsevier, pages 27-43.
    7. EHLERS, Lars & MAJUMDAR, Dipjyoti & MISHRA, Debasis & SEN, Arunava, 2016. "Continuity and incentive compatibility," Cahiers de recherche 2016-04, Universite de Montreal, Departement de sciences economiques.
    8. Tang, Qianfeng & Yu, Jingsheng, 2014. "A new perspective on Kesten's school choice with consent idea," Journal of Economic Theory, Elsevier, vol. 154(C), pages 543-561.

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