Towards More Expressive Cake Cutting
Ioannis Caragiannis, John Lai and Ariel Procaccia
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 are endowed with these expressive valuations, which is optimal in the sense that no 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.