# Obvious Manipulations in Cake-Cutting

## TL;DR

This paper explores the concept of non-obvious manipulability in cake-cutting, showing that certain mechanisms can be both fair and resistant to strategic manipulation in a less obvious way.

## Contribution

It introduces non-obvious manipulability as a weaker, more realistic strategic property and demonstrates that the leftmost leaves mechanism satisfies this with proportional fairness.

## Key findings

- Leftmost leaves mechanism is non-obviously manipulable and proportional.
- Most classical mechanisms are obviously manipulable, including the original moving knife.
- Non-obvious manipulability explains reduced manipulation in practice.

## Abstract

In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n=2 it implies a dictatorial allocation, whereas for n > 2 it requires that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril, called non-obvious manipulability, is compatible with the strong fairness property of proportionality, which guarantees that each agent receives 1/n of the cake. Both properties are satisfied by the leftmost leaves mechanism, an adaptation of the Dubins - Spanier moving knife procedure. Most other classical proportional mechanisms in literature are obviously manipulable, including the original moving knife mechanism. Non-obvious manipulability explains why leftmost leaves is manipulated less often in practice than other proportional mechanisms.