How to share a cake with a secret agent

TL;DR

This paper presents an algorithm for fair cake division among multiple agents with secret preferences, ensuring each gets at least their proportional share with an optimal number of cuts, even when preferences are unknown.

Contribution

It introduces a modified Even-Paz algorithm that handles secret preferences and guarantees connected shares with optimal cuts.

Findings

Algorithm guarantees each agent at least 1/n of the cake.

Number of cuts used is optimal at O(n log n).

Shares are connected and fair despite secret preferences.

Abstract

In this note we study a problem of fair division in the absence of full information. We give an algorithm which solves the following problem: n $\ge$ 2 persons want to cut a cake into n shares so that each person will get at least 1/n of the cake for his or her own measure, furthermore the preferences of one person are secret. How can we construct such shares? Our algorithm is a slight modification of the Even-Paz algorithm and allows to give a connected part to each agent. Moreover, the number of cuts used during the algorithm is optimal: O (n log(n)) .