---
title: "Towards More Expressive Cake Cutting"
authors:
  - "Ioannis Caragiannis"
  - "John K. Lai"
  - "Ariel D. Procaccia"
doi: "10.5591/978-1-57735-516-8/IJCAI11-033"
url: "https://ijcai.org/proceedings/2011/33"
pdf: "https://ijcai.org/proceedings/2011/0033.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "127-131"
track: ""
keywords:
---

# Towards More Expressive Cake Cutting

Ioannis Caragiannis, John K. Lai, Ariel D. Procaccia

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 127-131. DOI: [10.5591/978-1-57735-516-8/IJCAI11-033](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-033)

## Abstract

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.