Abstract
We consider the issue of fair division of goods, using the cake cutting abstraction, and aim to bound the possible degradation in social welfare due to the fairness requirements. Previous work has considered this problem for the setting where the division may allocate each player any number of unconnected pieces. Here, we consider the setting where each player must receive a single connected piece. For this setting, we provide tight bounds on the maximum possible degradation to both utilitarian and egalitarian welfare due to three fairness criteria — proportionality, envy-freeness and equitability.
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References
Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: FOCS, pp. 295–304 (2004)
Alon, N.: Splitting necklaces. Advances in Mathematics 63(3), 247–253 (1987)
Brams, S.J., Taylor, A.D.: An envy-free cake division protocol. The American Mathematical Monthly 102(1), 9–18 (1995)
Brams, S.J., Taylor, A.D.: Fair Division: From cake cutting to dispute resolution. Cambridge University Press, New York (1996)
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)
Dubins, L.E., Spanier, E.H.: How to cut a cake fairly. The American Mathematical Monthly 68(1), 1–17 (1961)
Even, S., Paz, A.: A note on cake cutting. Discrete Applied Mathematics 7(3), 285–296 (1984)
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)
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)
Moulin, H.J.: Fair Division and Collective Welfare. MIT Press Books, vol. 0262633116. MIT Press, Cambridge (2004)
Procaccia, A.D.: Thou shalt covet thy neighbor’s cake. In: IJCAI, pp. 239–244 (2009)
Robertson, J., Webb, W.: Cake-cutting algorithms: Be fair if you can. A K Peters, Ltd., Natick (1998)
Steinhaus, H.: Sur la division pragmatique. Econometrica 17(Supplement: Report of the Washington Meeting), 315–319 (1949)
Stromquist, W.: How to cut a cake fairly. The American Mathematical Monthly 87(8), 640–644 (1980)
Stromquist, W.: Envy-free cake divisions cannot be found by finite protocols. Electronic Journal of Combinatorics 15(1) (January 2008)
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)
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Aumann, Y., Dombb, Y. (2010). The Efficiency of Fair Division with Connected Pieces. In: Saberi, A. (eds) Internet and Network Economics. WINE 2010. Lecture Notes in Computer Science, vol 6484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17572-5_3
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DOI: https://doi.org/10.1007/978-3-642-17572-5_3
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