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We study the assignment problem of objects to agents with heterogeneous preferences under distributional constraints. Each agent is associated with a publicly known type and has a private ordinal ranking over objects. We are interested in…
We investigate the problem of random assignment of indivisible goods, in which each agent has an ordinal preference and a constraint. Our goal is to characterize the conditions under which there always exists a random assignment that…
We study the problem of assigning objects to agents in the presence of arbitrary linear constraints when agents are allowed to be indifferent between objects. Our main contribution is the generalization of the (Extended) Probabilistic…
Consider the problem of assigning indivisible objects to agents with strict ordinal preferences over objects, where each agent is interested in consuming at most one object, and objects have integer minimum and maximum quotas. We define an…
The Probabilistic Serial (PS) mechanism -- also known as the simultaneous eating algorithm -- is a canonical solution for the random assignment problem under ordinal preferences. It guarantees envy-freeness and ordinal efficiency in the…
We consider the multi-unit random assignment problem in which agents express preferences over objects and objects are allocated to agents randomly based on the preferences. The most well-established preference relation to compare random…
In the assignment problem, the goal is to assign indivisible items to agents who have ordinal preferences, efficiently and fairly, in a strategyproof manner. In practice, first-choice maximality, i.e., assigning a maximal number of agents…
We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of perishable resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and…
In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have…
We consider the discrete assignment problem in which agents express ordinal preferences over objects and these objects are allocated to the agents in a fair manner. We use the stochastic dominance relation between fractional or randomized…
Ensuring efficiency and envy-freeness in allocating indivisible goods without money often requires randomization. However, existing combinatorial assignment mechanisms (for applications such as course allocation, food banks, and refugee…
When allocating indivisible items to agents, it is known that the only strategyproof mechanisms that satisfy a set of rather mild conditions are constrained serial dictatorships: given a fixed order over agents, at each step the designated…
Priority-based allocation of individuals to positions are pervasive, and elimination of justified envy is often, an absolute requirement. This leaves serial dictatorship (SD) as the only rule that avoids justified envy under standard direct…
A principal has $m$ identical objects to allocate among a group of $n$ agents. Objects are desirable and the principal's value of assigning an object to an agent is the agent's private information. The principal can verify up to $k$ agents,…
We consider the allocation of indivisible objects when agents have preferences over their own allocations, but share the ownership of the resources to be distributed. Examples might include seats in public schools, faculty offices, and time…
We study the problem of assigning indivisible objects to agents where each is to receive at most one. To ensure fairness in the absence of monetary compensation, we consider random assignments. Random Priority, also known as Random Serial…
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…
Sequential allocation is a simple and widely studied mechanism to allocate indivisible items in turns to agents according to a pre-specified picking sequence of agents. At each turn, the current agent in the picking sequence picks its most…
In allocating objects via lotteries, it is common to consider ordinal rules that rely solely on how agents rank degenerate lotteries. While ordinality is often imposed due to cognitive or informational constraints, we provide another…
We consider the problem of fairly and efficiently allocating indivisible items (goods or bads) under capacity constraints. In this setting, we are given a set of categorized items. Each category has a capacity constraint (the same for all…