An Algorithmic Framework for Strategic Fair Division

TL;DR

This paper introduces a new algorithmic framework called Generalized Cut and Choose (GCC) protocols for fair division, ensuring strategic stability and fairness properties like proportionality and envy-freeness in cake cutting.

Contribution

The paper develops the GCC protocol class, analyzing its game-theoretic properties and demonstrating that equilibria align with fair division concepts such as proportionality and envy-freeness.

Findings

GCC protocols have approximate subgame perfect Nash equilibria.

Equilibria of proportional GCC protocols are approximately proportional.

A protocol is designed where Nash equilibria match envy-free allocations.

Abstract

We study the paradigmatic fair division problem of allocating a divisible good among agents with heterogeneous preferences, commonly known as cake cutting. Classical cake cutting protocols are susceptible to manipulation. Do their strategic outcomes still guarantee fairness? To address this question we adopt a novel algorithmic approach, by designing a concrete computational framework for fair division---the class of Generalized Cut and Choose (GCC) protocols}---and reasoning about the game-theoretic properties of algorithms that operate in this model. The class of GCC protocols includes the most important discrete cake cutting protocols, and turns out to be compatible with the study of fair division among strategic agents. In particular, GCC protocols are guaranteed to have approximate subgame perfect Nash equilibria, or even exact equilibria if the protocol's tie-breaking rule is flexible. We further observe that the (approximate) equilibria of proportional GCC protocols---which guarantee each of the $n$ agents a $1/n$-fraction of the cake---must be (approximately) proportional. Finally, we design a protocol in this framework with the property that its Nash equilibrium allocations coincide with the set of (contiguous) envy-free allocations.