627 research outputs found
Allocating Indivisible Items in Categorized Domains
Abstract We formulate a general class of allocation problems called categorized domain allocation problems (CDAPs), where indivisible items from multiple categories are allocated to agents without monetary transfer and each agent gets at least one item per category. We focus on basic CDAPs, where the number of items in each category equals to the number of agents. We characterize serial dictatorships for basic CDAPs by a minimal set of three desired properties: strategyproofness, non-bossiness, and category-wise neutrality. Then, we propose a natural extension of serial dictatorships called categorical sequential allocation mechanisms (CSAMs), which allocate the items in multiple rounds: in each round, the active agent chooses an item from a designated category. We fully characterize the worst-case ordinal efficiency of CSAMs for optimistic and pessimistic agents. We believe that these constitute a promising first step towards theoretical foundations and applications of general CDAPs
Fair Allocation of goods and chores -- Tutorial and Survey of Recent Results
Fair resource allocation is an important problem in many real-world
scenarios, where resources such as goods and chores must be allocated among
agents. In this survey, we delve into the intricacies of fair allocation,
focusing specifically on the challenges associated with indivisible resources.
We define fairness and efficiency within this context and thoroughly survey
existential results, algorithms, and approximations that satisfy various
fairness criteria, including envyfreeness, proportionality, MMS, and their
relaxations. Additionally, we discuss algorithms that achieve fairness and
efficiency, such as Pareto Optimality and Utilitarian Welfare. We also study
the computational complexity of these algorithms, the likelihood of finding
fair allocations, and the price of fairness for each fairness notion. We also
cover mixed instances of indivisible and divisible items and investigate
different valuation and allocation settings. By summarizing the
state-of-the-art research, this survey provides valuable insights into fair
resource allocation of indivisible goods and chores, highlighting computational
complexities, fairness guarantees, and trade-offs between fairness and
efficiency. It serves as a foundation for future advancements in this vital
field
Guaranteeing Envy-Freeness under Generalized Assignment Constraints
We study fair division of goods under the broad class of generalized
assignment constraints. In this constraint framework, the sizes and values of
the goods are agent-specific, and one needs to allocate the goods among the
agents fairly while further ensuring that each agent receives a bundle of total
size at most the corresponding budget of the agent. Since, in such a constraint
setting, it may not always be feasible to partition all the goods among the
agents, we conform -- as in recent works -- to the construct of charity to
designate the set of unassigned goods. For this allocation framework, we obtain
existential and computational guarantees for envy-free (appropriately defined)
allocation of divisible and indivisible goods, respectively, among agents with
individual, additive valuations for the goods.
We deem allocations to be fair by evaluating envy only with respect to
feasible subsets. In particular, an allocation is said to be feasibly envy-free
(FEF) iff each agent prefers its bundle over every (budget) feasible subset
within any other agent's bundle (and within the charity). The current work
establishes that, for divisible goods, FEF allocations are guaranteed to exist
and can be computed efficiently under generalized assignment constraints.
In the context of indivisible goods, FEF allocations do not necessarily
exist, and hence, we consider the fairness notion of feasible envy-freeness up
to any good (FEFx). We show that, under generalized assignment constraints, an
FEFx allocation of indivisible goods always exists. In fact, our FEFx result
resolves open problems posed in prior works. Further, for indivisible goods and
under generalized assignment constraints, we provide a pseudo-polynomial time
algorithm for computing FEFx allocations, and a fully polynomial-time
approximation scheme (FPTAS) for computing approximate FEFx allocations.Comment: 29 page
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