Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations
Haris Aziz, Chun Ye

TL;DR
This paper introduces new algorithms for fair cake cutting with piecewise constant and uniform valuations, achieving properties like envy-freeness, Pareto optimality, and strategyproofness, with some algorithms being polynomial-time and robust.
Contribution
It presents robust, efficient, and strategyproof cake cutting algorithms tailored for piecewise constant and uniform valuations, extending previous work with new properties and implementations.
Findings
CCEA is polynomial-time, envy-free, and non-wasteful.
MEA achieves envy-freeness, proportionality, and Pareto optimality.
CSD satisfies strategyproofness in expectation and robust proportionality.
Abstract
Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also…
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications · Experimental Behavioral Economics Studies
