In Fall 2024 I took an algorithmic game theory course offered by professor Shuchi Chawla and one of the topics we covered was the field of fair-division. In my course project, I collaborated with Alejandro Leos to create an in-depth research overview of the field of envy-free cake cutting.

The core concept behind envy-free cake cutting revolves around dividing a single, potentially heterogeneous resource (the “cake”) among \(n\) agents in a manner that satisfies the following criteria:

Disjoint Allocations: Each agent receives a distinct portion of the cake, and no two agents share any part of the resource.
Completeness: The entire cake is allocated, leaving no portion unassigned.
Envy-Freeness : No agent prefers another agent’s allocation over their own. In other words, each agent perceives their allocation as the “best” of the realized allocations.

This final condition, envy-freeness, ensures a “fair” allocation and is particularly challenging to achieve when the cake is heterogeneous and agents have different preferences over the segments of the cake.

Developing algorithms and protocols that guarantee envy-free allocations is a complex and active area of research in algorithmic game theory. In our work, Alejandro and I conducted a comprehensive literature review of envy-free cake cutting algorithms, analyzing the state-of-the-art protocols and their strengths and limitations. We also explored promising future research directions and presented preliminary ideas for advancing the field.