Related papers: Dividing a Graphical Cake
We consider allocating indivisible goods with provable fairness guarantees that are satisfied regardless of which bundle of items each agent receives. Symmetrical allocations of this type are known to exist for divisible resources, such as…
Envy-free cake-cutting protocols procedurally divide an infinitely divisible good among a set of agents so that no agent prefers another's allocation to their own. These protocols are highly complex and difficult to prove correct. Recently,…
We study the computational complexity of finding fair allocations of indivisible goods in the setting where a social network on the agents is given. Notions of fairness in this context are "localized", that is, agents are only concerned…
We study searching and sorting in rounds motivated by a fair division question: given a cake cutting problem with $n$ players, compute a fair allocation in at most $k$ rounds of interaction with the players. Rounds interpolate between the…
The problem of fair division of indivisible goods is a fundamental problem of social choice. Recently, the problem was extended to the case when goods form a graph and the goal is to allocate goods to agents so that each agent's bundle…
We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which…
In fair division of a connected graph $G = (V, E)$, each of $n$ agents receives a share of $G$'s vertex set $V$. These shares partition $V$, with each share required to induce a connected subgraph. Agents use their own valuation functions…
There is arbitrariness in optimum solutions of graph-theoretic problems that can give rise to unfairness. Incorporating fairness in such problems, however, can be done in multiple ways. For instance, fairness can be defined on an individual…
The design of algorithms for political redistricting generally takes one of two approaches: optimize an objective such as compactness or, drawing on fair division, construct a protocol whose outcomes guarantee partisan fairness. We aim to…
We study the cake-cutting problem when agents have single-peaked preferences over the cake. We show that a recently proposed mechanism by Wang-Wu (2019) to obtain envy-free allocations can yield large welfare losses. Using a simplifying…
We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity…
We study the existence of fair distributions when we have more guests than pieces to allocate, focusing on envy-free distributions among those who receive a piece. The conditions on the demand from the guests can be weakened from those of…
We consider the classic cake-cutting problem of producing envy-free allocations, restricted to the case of four agents. The problem asks for a partition of the cake to four agents, so that every agent finds her piece at least as valuable as…
We study classic fair-division problems in a partial information setting. This paper respectively addresses fair division of rent, cake, and indivisible goods among agents with cardinal preferences. We will show that, for all of these…
In this article we propose a probabilistic framework in order to study the fair division of a divisible good, e.g., a cake, between n players. Our framework follows the same idea than the ''Full independence model'' used in the study of…
Fair division with unequal shares is an intensively studied recourse allocation problem. For $ i\in [n] $, let $ \mu_i $ be an atomless probability measure on the measurable space $(C,\mathcal{S}) $ and let $ t_i $ be positive numbers…
Fair division considers the allocation of scarce resources among agents in such a way that every agent gets a fair share. It is a fundamental problem in society and has received significant attention and rapid developments from the game…
This article deals with the cake cutting problem. In this setting, there exists two notions of fair division: proportional division (when there are n players, each player thinks to get at least 1/n of the cake) and envy-free division (each…
A set of objects is to be divided fairly among agents with different tastes, modeled by additive utility-functions. If we consider the objects as indivisible, many instances of the decision problem: ``Is there a fair division of the objects…
We study the allocation of indivisible items that form an undirected graph and investigate the worst-case welfare loss when requiring that each agent must receive a connected subgraph. Our focus is on both egalitarian and utilitarian…