Throw One’s Cake — and Eat It Too

  • Orit Arzi
  • Yonatan Aumann
  • Yair Dombb
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6982)

Abstract

We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here, we show that in some cases, discarding some of the cake and fairly dividing only the remainder may be socially preferable to any fair division of the entire cake. We study this phenomenon, providing asymptotically-tight bounds on the social improvement achievable by such discarding.

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References

  1. 1.
    Aumann, Y., Dombb, Y.: The efficiency of fair division with connected pieces. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 26–37. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Brams, S.J., Taylor, A.D.: An envy-free cake division protocol. The American Mathematical Monthly 102(1), 9–18 (1995)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Brams, S.J., Taylor, A.D.: Fair Division: From cake cutting to dispute resolution. Cambridge University Press, New York (1996)MATHCrossRefGoogle Scholar
  4. 4.
    Caragiannis, I., Kaklamanis, C., Kanellopoulos, P., Kyropoulou, M.: The efficiency of fair division. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 475–482. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Caragiannis, I., Lai, J., Procaccia, A.: Towards more expressive cake cutting. In: IJCAI: International Joint Conferences on Artificial Intelligence (2011)Google Scholar
  6. 6.
    Chen, Y., Lai, J., Parkes, D.C., Procaccia, A.D.: Truth, justice, and cake cutting. In: AAAI (2010)Google Scholar
  7. 7.
    Dubins, L.E., Spanier, E.H.: How to cut a cake fairly. The American Mathematical Monthly 68(1), 1–17 (1961)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Edmonds, J., Pruhs, K.: Cake cutting really is not a piece of cake. In: SODA 2006: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, pp. 271–278. ACM, New York (2006)CrossRefGoogle Scholar
  9. 9.
    Even, S., Paz, A.: A note on cake cutting. Discrete Applied Mathematics 7(3), 285–296 (1984)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Magdon-Ismail, M., Busch, C., Krishnamoorthy, M.S.: Cake-cutting is not a piece of cake. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 596–607. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Moulin, H.J.: Fair Division and Collective Welfare. Number 0262633116 in MIT Press Books. The MIT Press (2004)Google Scholar
  12. 12.
    Procaccia, A.D.: Thou shalt covet thy neighbor’s cake. In: IJCAI, pp. 239–244 (2009)Google Scholar
  13. 13.
    Robertson, J., Webb, W.: Cake-cutting algorithms: Be fair if you can. A K Peters, Ltd., Natick (1998)MATHGoogle Scholar
  14. 14.
    Sgall, J., Woeginger, G.J.: A lower bound for cake cutting. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 459–469. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  15. 15.
    Steinhaus, H.: Sur la division pragmatique. Econometrica 17(Supplement: Report of the Washington Meeting), 315–319 (1949)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Stromquist, W.: How to cut a cake fairly. The American Mathematical Monthly 87(8), 640–644 (1980)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Orit Arzi
    • 1
  • Yonatan Aumann
    • 1
  • Yair Dombb
    • 1
  1. 1.Department of Computer ScienceBar-Ilan UniversityRamat GanIsrael

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