A Discrete and Bounded Envy-free Cake Cutting Protocol for Four Agents

TL;DR

This paper introduces a discrete, bounded envy-free cake cutting protocol specifically designed for four agents, addressing a longstanding open problem in fair division.

Contribution

It presents the first known discrete and bounded envy-free protocol for four agents, advancing the theoretical understanding of fair division algorithms.

Findings

Provides a finite protocol for four-agent envy-free cake cutting

Ensures envy-freeness with minimal queries

Addresses a fifty-year open problem in the field

Abstract

We consider the well-studied cake cutting problem in which the goal is to identify a fair allocation based on a minimal number of queries from the agents. The problem has attracted considerable attention within various branches of computer science, mathematics, and economics. Although, the elegant Selfridge-Conway envy-free protocol for three agents has been known since 1960, it has been a major open problem for the last fifty years to obtain a bounded envy-free protocol for more than three agents. We propose a discrete and bounded envy-free protocol for four agents.