Fair Cake Division Under Monotone Likelihood Ratios

References

• [1] Alijani R, Farhadi M, Ghodsi M, Seddighin M, Tajik AS (2017) Envy-free mechanisms with minimum number of cuts. Proc. 31st AAAI Conf. on Artificial Intelligence.Google Scholar
• [2] Alon N (1987) Splitting necklaces. Adv. Math. 63(3):247–253.Crossref, Google Scholar
• [3] Arunachaleswaran ER, Barman S, Kumar R, Rathi N (2019) Fair and efficient cake division with connected pieces. Proc. Internat. Conf. on Web and Internet Economics (Springer, Berlin), 57–70.Google Scholar
• [4] Athey S (2001) Single crossing properties and the existence of pure strategy equilibria in games of incomplete information. Econometrica 69(4):861–889.Crossref, Google Scholar
• [5] Aumann Y, Dombb Y, Hassidim A (2013) Computing socially-efficient cake divisions. Proc. Internat. Conf. on Autonomous Agents and Multi-Agent Systems (International Foundation for Autonomous Agents and Multiagent Systems), 343–350.Google Scholar
• [6] Aziz H, Mackenzie S (2016) A discrete and bounded envy-free cake cutting protocol for any number of agents. Proc. IEEE 57th Annual Sympos. Foundations Comput. Sci. (IEEE, New York), 416–427.Google Scholar
• [7] Bei X, Chen N, Hua X, Tao B, Yang E (2012) Optimal proportional cake cutting with connected pieces. Proc. 26th AAAI Conf. on Artificial Intelligence.Google Scholar
• [8] Brams SJ, Taylor AD (1995) An envy-free cake division protocol. Amer. Math. Monthly 102(1):9–18.Crossref, Google Scholar
• [9] Brams SJ, Taylor AD (1996) Fair Division: From Cake-Cutting to Dispute Resolution (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
• [10] Brânzei S, Nisan N (2017) The query complexity of cake cutting. Preprint, submitted May 8; revised July 13, 2018, https://arxiv.org/abs/1705.02946.Google Scholar
• [11] Casella G, Berger RL (2002) Statistical Inference, vol. 2 (Duxbury, Pacific Grove, CA).Google Scholar
• [12] Cechlárová K, Pillárová E (2012) On the computability of equitable divisions. Discrete Optim. 9(4):249–257.Crossref, Google Scholar
• [13] Chen Y, Lai JK, Parkes DC, Procaccia AD (2013) Truth, justice, and cake cutting. Games Econom. Behav. 77(1):284–297.Crossref, Google Scholar
• [14] Cohler YJ, Lai JK, Parkes DC, Procaccia AD (2011) Optimal envy-free cake cutting. Proc. 25th AAAI Conf. on Artificial Intelligence.Google Scholar
• [15] Deng X, Qi Q, Saberi A (2012) Algorithmic solutions for envy-free cake cutting. Oper. Res. 60(6):1461–1476.Link, Google Scholar
• [16] Dubins LE, Spanier EH (1961) How to cut a cake fairly. Amer. Math. Monthly 68(1P1):1–17.Crossref, Google Scholar
• [17] Foley DK (1967) Resource Allocation and the Public Sector, vol. 7 (Yale University, New Haven, CT), 45–98.Google Scholar
• [18] Gamow G, Stern M (1958) Puzzle-Math. (Viking Adult). http://www.worldcat.org/isbn/0670583359.Google Scholar
• [19] Gans JS, Smart M (1996) Majority voting with single-crossing preferences. J. Public Econom. 59(2):219–237.Crossref, Google Scholar
• [20] Grötschel M, Lovász L, Schrijver A (2012) Geometric Algorithms and Combinatorial Optimization, vol. 2 (Springer Science & Business Media, New York).Google Scholar
• [21] Hollender A, Goldberg P, Suksompong W (2020) Contiguous cake cutting: Hardness results and approximation algorithms. J. Artificial Intelligence Res. 69:109–141.Google Scholar
• [22] Jewitt I (1991) Applications of likelihood ratio orderings in economics. Stochastic Orders and Decision under Risk. Lecture Notes Monograph Series, vol. 19 (Institute of Mathematical Sciences), 174–189.Google Scholar
• [23] Kaneko M, Nakamura K (1979) The Nash social welfare function. Econometrica: J. Econometric Soc. (JSTOR) 47(2):423–435.Google Scholar
• [24] Kurokawa D, Lai JK, Procaccia AD (2013) How to cut a cake before the party ends. Proc. 27th AAAI Conf. on Artificial Intelligence.Google Scholar
• [25] Larsen RJ, Marx ML (2001) An Introduction to Mathematical Statistics and Its Applications, vol. 5. (Prentice Hall, Upper Saddle River, NJ).Google Scholar
• [26] Lipton RJ, Markakis E, Mossel E, Saberi A (2004) On approximately fair allocations of indivisible goods. Proc. 5th ACM Conf. on Electronic Commerce (ACM, New York), 125–131.Google Scholar
• [27] Mossel E, Tamuz O (2010) Truthful fair division. Proc. Internat. Sympos. on Algorithmic Game Theory (Springer, Berlin), 288–299.Google Scholar
• [28] Moulin H (2004) Fair Division and Collective Welfare (MIT Press, Cambridge, MA).Google Scholar
• [29] Nash JF Jr (1950) The bargaining problem. Econometrica: J. Econometric Soc. 18(2):155–162.Google Scholar
• [30] Procaccia AD (2016) Cake cutting algorithms (Chapter 13). Brandt F, Conitzer V, Endriss U, Lang J, Procaccia AD, eds. Handbook of Computational Social Choice (Cambridge University Press, Cambridge, MA), 311–332.Google Scholar
• [31] Robertson J, Webb W (1998) Cake-Cutting Algorithms: Be Fair if You Can (AK Peters/CRC Press, Boca Raton, FL).Crossref, Google Scholar
• [32] Saumard A, Wellner JA (2014) Log-concavity and strong log-concavity: A review. Statist. Surveys 8:45.Crossref, Google Scholar
• [33] Steinhaus H (1948) The problem of fair division. Econometrica 16:101–104.Google Scholar
• [34] Stromquist W (1980) How to cut a cake fairly. Amer. Math. Monthly 87(8):640–644.Crossref, Google Scholar
• [35] Stromquist W (2008) Envy-free cake divisions cannot be found by finite protocols. Electronic J. Combinatorics 15(1):11.Crossref, Google Scholar
• [36] Su FE (1999) Rental harmony: Sperner’s lemma in fair division. Amer. Math. Monthly 106(10):930–942.Crossref, Google Scholar
• [37] Wang C, Wu X (2019) Cake cutting with single-peaked valuations. Proc. Internat. Conf. Combinatorial Optimization Applications (Springer, Berlin), 507–516.Google Scholar
• [38] Weller D (1985) Fair division of a measurable space. J. Math. Econom. 14(1):5–17.Crossref, Google Scholar