Fairly Dividing a Cake after Some Parts Were Burnt in the Oven

Abstract

There is a heterogeneous resource that contains both good parts and bad parts, for example, a cake with some parts burnt, a land-estate with some parts heavily taxed, or a chore with some parts fun to do. The resource has to be divided fairly among $n$ agents with different preferences, each of whom has a personal value-density function on the resource. The value-density functions can accept any real value --- positive, negative or zero. Each agent should receive a connected piece and no agent should envy another agent. We prove that such a division exists for 3 agents and present preliminary positive results for larger numbers of agents.

Extended version of AAMAS-18 paper. Contains preliminary results indicating that the conjecture is true in two special cases (Section 6)

References in corpus (2)

• Fair and Square: Cake-Cutting in Two Dimensions
• Around Sperner's lemma

Cited by in corpus (6)

• Fair allocation of combinations of indivisible goods and chores
• Mixed Fair Division: A Survey
• Efficient Fair Division with Minimal Sharing
• Cutting a Cake Fairly for Groups Revisited
• Equitable Allocations of Indivisible Goods
• Guarantees in Fair Division: general or monotone preferences