Cake cutting really is not a piece of cake
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A theory of expressiveness in mechanisms
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Thou shalt covet thy neighbor's cake
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Throw one's cake: and eat it too
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Equilibrium analysis in cake cutting
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Cake cutting is a playful name for the problem of fairly dividing a heterogeneous divisible good among a set of agents. The agent valuations for different pieces of cake are typically assumed to be additive. However, in certain practical settings this assumption is invalid because agents may not have positive value for arbitrarily small "crumbs" of cake. In this paper, we propose a new, more expressive model of agent valuations that captures this feature. We present an approximately proportional algorithm for any number of agents that have such expressive valuations. The algorithm is optimal in the sense that no other algorithm can guarantee a greater worst-case degree of proportionality. We also design an optimal approximately proportional and fully envy-free algorithm for two agents