On the existence of equitable cake divisions

Authors:
KatarıNa CechláRová;Jozef Doboš;Eva PilláRová
Affiliations:
Institute of Mathematics, Faculty of Science, P.J. Šafárik University, Jesenná 5, 040 01 Košice, Slovakia;Institute of Mathematics, Faculty of Science, P.J. Šafárik University, Jesenná 5, 040 01 Košice, Slovakia;Institute of Mathematics, Faculty of Science, P.J. Šafárik University, Jesenná 5, 040 01 Košice, Slovakia
Venue:
Information Sciences: an International Journal
Year:
2013

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The efficiency of fair division with connected pieces

WINE'10 Proceedings of the 6th international conference on Internet and network economics

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Abstract

Let the cake be represented by the unit interval and let each player have a valuation expressed by a nonatomic probability measure. A cake division is said to be equitable if the value of the piece assigned to a player by his measure is the same for all players. We show that for any number n of players in any order an equitable division exists, giving each player a contiguous cake piece. Moreover, there is at least one order in which the common value is not smaller than 1/n.