Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
On approximately fair allocations of indivisible goods
EC '04 Proceedings of the 5th ACM conference on Electronic commerce
On Low-Envy Truthful Allocations
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
On worst-case allocations in the presence of indivisible goods
WINE'11 Proceedings of the 7th international conference on Internet and Network Economics
Incentive compatible two player cake cutting
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Mechanism design for fair division: allocating divisible items without payments
Proceedings of the fourteenth ACM conference on Electronic commerce
Cake cutting: not just child's play
Communications of the ACM
Equilibrium analysis in cake cutting
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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We address the problem of fair division, or cake cutting, with the goal of finding truthful mechanisms. In the case of a general measure space ("cake") and non-atomic, additive individual preference measures - or utilities - we show that there exists a truthful "mechanism" which ensures that each of the k players gets at least 1/k of the cake. This mechanism also minimizes risk for truthful players. Furthermore, in the case where there exist at least two different measures we present a different truthful mechanism which ensures that each of the players gets more than 1/k of the cake. We then turn our attention to partitions of indivisible goods with bounded utilities and a large number of goods. Here we provide similar mechanisms, but with slightly weaker guarantees. These guarantees converge to those obtained in the non-atomic case as the number of goods goes to infinity.