Advertisement

Social Choice and Welfare

, Volume 48, Issue 1, pp 31–57 | Cite as

Efficient lottery design

  • Onur KestenEmail author
  • Morimitsu Kurino
  • Alexander S. Nesterov
Original Paper

Abstract

There has been a surge of interest in stochastic assignment mechanisms that have proven to be theoretically compelling thanks to their prominent welfare properties. Contrary to stochastic mechanisms, however, lottery mechanisms are commonly used in real life for indivisible goods allocation. To help facilitate the design of practical lottery mechanisms, we provide new tools for obtaining stochastic improvements in lotteries. As applications, we propose lottery mechanisms that improve upon the widely used random serial dictatorship mechanism and a lottery representation of its competitor, the probabilistic serial mechanism. The tools we provide here can be useful in developing welfare-enhanced new lottery mechanisms for practical applications such as school choice.

References

  1. Abdulkadiroğlu A, Sönmez T (1998) Random serial dictatorship and the core from random endowments in house allocation problems. Econometrica 66:689–701CrossRefGoogle Scholar
  2. Abdulkadiroğlu A, Sönmez T (2003) Ordinal efficiency and dominated sets of assignments. J Econ Theory 112:157–172CrossRefGoogle Scholar
  3. Abdulkadiroğlu A, Sönmez T (2003) School choice: a mechanism design approach. Am Econ Rev 93:729–747CrossRefGoogle Scholar
  4. Athanassoglou S, Sethuraman J (2011) House allocation with fractional endowments. Int J Game Theory 40:481–513CrossRefGoogle Scholar
  5. Birkhoff G (1946) Three observations on linear algebra. Revi Univ Nac Tucuman Ser A 5:147–151Google Scholar
  6. Bogomolnaia A, Moulin H (2001) A new solution to the random assignment problem. J Econ Theory 100:295–328CrossRefGoogle Scholar
  7. Budish E, Che Y-K, Kojima F, Milgrom P (2013) Designing random allocation mechanisms: theory and applications. Am Econ Rev 103:585–623CrossRefGoogle Scholar
  8. Che Y-K, Kojima F (2010) Asymptotic equivalence of random priority and probabilistic serial mechainsms. Econometrica 78:1625–1672CrossRefGoogle Scholar
  9. Erdil A (2014) Strategy-proof stochastic assignment. J Econ Theory 151:146–162CrossRefGoogle Scholar
  10. Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Monthly 69:9–15CrossRefGoogle Scholar
  11. Hashimoto T, Hirata D, Kesten O, Kurino M, Ünver MU (2014) Two axiomatic approaches to the probabilistic serial mechanism. Theor Econ 9:253–277CrossRefGoogle Scholar
  12. Hugh-Jones D, Kurino M, Vanberg C (2014) An experimental study on the incentives of the probabilistic serial mechanism. Games Econ Behav 87:367–380CrossRefGoogle Scholar
  13. Kesten O (2009) Why do popular mechanisms lack efficiency in random environments? J Econ Theory 144:2209–2226CrossRefGoogle Scholar
  14. Kesten O, Ünver MU (2015) A theory of school-choice lotteries. Theor Econ 10:543–595CrossRefGoogle Scholar
  15. Kojima F (2009) Random assignment of multiple indivisible objects. Math Soc Sci 57:134–142CrossRefGoogle Scholar
  16. Kojima F, Manea M (2010) Incentives in the probabilistic serial mechanism. J Econ Theory 144:106–123CrossRefGoogle Scholar
  17. Manea M (2008) Random serial dictatorship and ordinally efficient contracts. Int J Game Theory 36:489–496CrossRefGoogle Scholar
  18. Manea M (2009) Asymptotic ordinal inefficiency of random serial dictatorship. Theor Econ 4:165–197Google Scholar
  19. Nesterov AS (2014) Fairness and efficiency in a random assignment. WZB Discussion PaperGoogle Scholar
  20. Shapley L, Scarf H (1974) On cores and indivisibility. J Math Econ 1:23–37CrossRefGoogle Scholar
  21. von Neumann J (1953) A certain zero-sum two-person game equivalent to the optimal assignment problem. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games, vol 2. Princeton University Press, Princeton, New JerseyGoogle Scholar
  22. Zhou L (1990) On a conjecture by Gale about one-sided matching problems. J Econ Theory 52:123–135CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Onur Kesten
    • 1
    Email author
  • Morimitsu Kurino
    • 2
  • Alexander S. Nesterov
    • 3
  1. 1.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA
  2. 2.Faculty of Engineering, Information and SystemsUniversity of TsukubaTsukubaJapan
  3. 3.WZBBerlinGermany

Personalised recommendations