Related papers: Achieving rental harmony with a secretive roommate

We study the classic problem of fairly allocating a set of indivisible goods among a group of agents, and focus on the notion of approximate proportionality known as PROPm. Prior work showed that there exists an allocation that satisfies…

We study mechanisms for an allocation of goods among agents, where agents have no incentive to lie about their true values (incentive compatible) and for which no agent will seek to exchange outcomes with another (envy-free). Mechanisms…

We consider a multi-agent resource allocation setting in which an agent's utility may decrease or increase when an item is allocated. We take the group envy-freeness concept that is well-established in the literature and present stronger…

Neural networks have shown state-of-the-art performance in designing auctions, where the network learns the optimal allocations and payment rule to ensure desirable properties. Motivated by the same, we focus on learning fair division of…

A well-regarded fairness notion when dividing indivisible chores is envy-freeness up to one item (EF1), which requires that pairwise envy can be eliminated by the removal of a single item. While an EF1 and Pareto optimal (PO) allocation of…

We investigate the tradeoffs between fairness and efficiency when allocating indivisible items over time. Suppose T items arrive over time and must be allocated upon arrival, immediately and irrevocably, to one of n agents. Agent i assigns…

We divide efficiently a pile of indivisible goods in common property, using cash transfers to ensure fairness among agents with utility linear in money. We compare three cognitively feasible and privacy preserving division rules in terms of…

We study popular matchings in three classical settings: the house allocation problem, the marriage problem, and the roommates problem. In the popular matching problem, (a subset of) the vertices in a graph have preference orderings over…

This paper extends the classic cake-cutting problem to a situation in which the "cake" is divided among families. Each piece of cake is owned and used simultaneously by all members of the family. A typical example of such a cake is land. We…

In the Stable Roommates problem, we seek a stable matching of the agents into pairs, in which no two agents have an incentive to deviate from their assignment. It is well known that a stable matching is unlikely to exist, but a stable…

We consider stability concepts for random matchings where agents have preferences over objects and objects have priorities for the agents. When matchings are deterministic, the standard stability concept also captures the fairness property…

Current work in planning with preferences assume that the user's preference models are completely specified and aim to search for a single solution plan. In many real-world planning scenarios, however, the user probably cannot provide any…

We study fair division of divisible goods under generalized assignment constraints. Here, each good has an agent-specific value and size, and every agent has a budget constraint that limits the total size of the goods she can receive. Since…

We investigate the query complexity of the fair allocation of indivisible goods. For two agents with arbitrary monotonic utilities, we design an algorithm that computes an allocation satisfying envy-freeness up to one good (EF1), a…

We consider Brouwer's fixed point theorem and Sperner's lemma in one dimension. We present a proof of the Brouwer theorem using the Sperner lemma, and vice versa. However, we also show that they are not equivalent, because the Sperner lemma…

We give an elementary proof of Brouwer's fixed-point theorem. The only mathematical prerequisite is a version of the Bolzano-Weierstrass theorem: a sequence in a compact subset of $n$-dimensional Euclidean space has a convergent subsequence…

It is challenging to quantify numerical preferences for different objectives in a multi-objective decision-making problem. However, the demonstrations of a user are often accessible. We propose an algorithm to infer linear preference…

The stable roommates problem is a non-bipartite version of the well-known stable matching problem. Teo and Sethuraman proved that, for each instance of the stable roommates problem in a complete graph, there exists a linear inequality…

We study the fundamental problem of allocating indivisible goods to agents with additive preferences. We consider eliciting from each agent only a ranking of her $k$ most preferred goods instead of her full cardinal valuations. We…

We conduct a computational analysis of fair and optimal partitions in additively separable hedonic games. We show that, for strict preferences, a Pareto optimal partition can be found in polynomial time while verifying whether a given…