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We investigate the fair allocation of indivisible goods to agents with possibly different entitlements represented by weights. Previous work has shown that guarantees for additive valuations with existing envy-based notions cannot be…

We initiate the study of indivisible chore allocation for agents with asymmetric shares. The fairness concept we focus on is the weighted natural generalization of maxmin share: WMMS fairness and OWMMS fairness. We first highlight the fact…

We consider the problem of assigning items to platforms where each item has a utility associated with each of the platforms to which it can be assigned. Each platform has a soft constraint over the total number of items it serves, modeled…

Social utility maximization refers to the process of allocating resources in such a way that the sum of agents' utilities is maximized under the system constraints. Such allocation arises in several problems in the general area of…

We consider the multiwinner election problem where the goal is to choose a committee of $k$ candidates given the voters' utility functions. We allow arbitrary additional constraints on the chosen committee, and the utilities of voters to…

We study the problem of computing maximin share guarantees, a recently introduced fairness notion. Given a set of $n$ agents and a set of goods, the maximin share of a single agent is the best that she can guarantee to herself, if she would…

We study a general allocation setting where agent valuations are concave additive. In this model, a collection of items must be uniquely distributed among a set of agents, where each agent-item pair has a specified utility. The objective is…

We study the question of dividing a collection of indivisible goods amongst a set of agents. The main objective of research in the area is to achieve one of two goals: fairness or efficiency. On the fairness side, envy-freeness is the…

A fundamental shortcoming of the concept of Nash equilibrium is its computational intractability: approximating Nash equilibria in normal-form games is PPAD-hard. In this paper, inspired by the ideas of smoothed analysis, we introduce a…

The problem of finding envy-free allocations of indivisible goods can not always be solved; therefore, it is common to study some relaxations such as envy-free up to one good (EF1). Another property of interest for efficiency of an…

A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate…

In this paper, we address the challenge of Nash equilibrium (NE) seeking in non-cooperative convex games with partial-decision information. We propose a distributed algorithm, where each agent refines its strategy through projected-gradient…

We consider a multi-agent resource allocation setting that models the assignment of papers to reviewers. A recurring issue in allocation problems is the compatibility of welfare/efficiency and fairness. Given an oracle to find a…

In this paper, we address \ac{SGNEP} seeking with risk-neutral agents. Our main contribution lies the development of a stochastic variance-reduced gradient (SVRG) technique, modified to contend with general sample spaces, within a…

The $\alpha$-fair resource allocation problem has received remarkable attention and has been studied in numerous application fields. Several algorithms have been proposed in the context of $\alpha$-fair resource sharing to distributively…

We study the problem of allocating $m$ indivisible goods among $n$ agents, where each agent's valuation is fractionally subadditive (XOS). With respect to AnyPrice Share (APS) fairness, Kulkarni et al. (2024) showed that, when agents have…

Finding Nash equilibria in two-player zero-sum imperfect-information games remains a central challenge in multi-agent reinforcement learning. Recent multi-round regularization methods offer a promising direction, yet existing approaches…

We study the max-min fair allocation problem in which a set of $m$ indivisible items are to be distributed among $n$ agents such that the minimum utility among all agents is maximized. In the restricted setting, the utility of each item $j$…

The fair division of resources is an important age-old problem that has led to a rich body of literature. At the center of this literature lies the question of whether there exist fair mechanisms despite strategic behavior of the agents. A…

In this report we construct two mechanisms that fully implement social welfare maximising allocation in Nash equilibria for the case of a single infinitely divisible good subject to multiple inequality constraints. The first mechanism…