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The probabilistic serial mechanism with private endowments

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  • YIlmaz, Özgür

Abstract

A random assignment is ordinally efficient if it is not stochastically dominated with respect to individual preferences over sure objects. When there are no private endowments, the set of ordinally efficient random assignments is characterized by the eating algorithm (Bogomolnaia and Moulin, 2001). When there are private endowments, the main requirement is individual rationality; however, the eating algorithm fails to deliver this property. Our contribution is the natural generalization of the eating algorithm for this general class of problems. The family of this generalized eating algorithm characterizes the set of individually rational and ordinally efficient random assignments. A special solution in this family, the individually rational probabilistic serial (PSIR), also achieves a new fairness axiom, no justified-envy. However, it is not immune to strategic manipulation. We show that individual rationality, no justified-envy and strategy-proofness are incompatible.

Suggested Citation

  • YIlmaz, Özgür, 2010. "The probabilistic serial mechanism with private endowments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 475-491, July.
  • Handle: RePEc:eee:gamebe:v:69:y:2010:i:2:p:475-491
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    Cited by:

    1. Le, Phuong, 2013. "Competitive Equilibrium in the Random Assignment Problem," MPRA Paper 66290, University Library of Munich, Germany.
    2. repec:bla:ijethy:v:13:y:2017:i:4:p:369-385 is not listed on IDEAS
    3. Kesten, Onur & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    4. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    5. Özgün Ekici & Onur Kesten, 2016. "An equilibrium analysis of the probabilistic serial mechanism," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 655-674, August.
    6. 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.
    7. repec:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1059-3 is not listed on IDEAS
    8. repec:eee:matsoc:v:90:y:2017:i:c:p:56-62 is not listed on IDEAS
    9. Alcalde, Jose & Silva-Reus, José Ángel, 2013. "Allocating via Priorities," QM&ET Working Papers 13-3, University of Alicante, D. Quantitative Methods and Economic Theory.

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