On the Complexity of Efficiency and Envy-Freeness in Fair Division of Indivisible Goods with Additive Preferences
نویسندگان
چکیده
We study the problem of allocating a set of indivisible goods to a set of agents having additive preferences. We introduce two new important complexity results concerning efficiency and fairness in resource allocation problems: we prove that the problem of deciding whether a given allocation is Pareto-optimal is coNP-complete, and that the problem of deciding whether there is a Pareto-efficient and envy-free allocation is Σ 2 -complete.
منابع مشابه
Efficiency and envy-freeness in fair division of indivisible goods: logical representation and complexity
We consider the problem of allocating fairly a set of indivisible goods among agents from the point of view of compact representation and computational complexity. We start by assuming that agents have dichotomous preferences expressed by propositional formulae. We express efficiency and envy-freeness in a logical setting, which reveals unexpected connections to nonmonotonic reasoning. Then we ...
متن کاملAlmost Envy-Freeness with General Valuations
e goal of fair division is to distribute resources among competing players in a “fair” way. Envy-freeness is the most extensively studied fairness notion in fair division. Envy-free allocations do not always exist with indivisible goods, motivating the study of relaxed versions of envy-freeness. We study the envy-freeness up to any good (EFX) property, which states that no player prefers the b...
متن کاملCommunication Complexity of Discrete Fair Division
We initiate the study of the communication complexity of fair division with indivisible goods. We focus on the most well-studied fairness notions (envy-freeness, proportionality, and approximations thereof) and valuation classes (submodular, subadditive and unrestricted). Our results completely resolve whether the communication complexity of computing a fair allocation (or determining that none...
متن کاملDistributed fair allocation of indivisible goods
Distributed mechanisms for allocating indivisible goods are mechanisms lacking central control, in which agents can locally agree on deals to exchange some of the goods in their possession. We study convergence properties for such distributed mechanisms when used as fair division procedures. Specifically, we identify sets of assumptions under which any sequence of deals meeting certain conditio...
متن کاملDemocratic Fair Allocation of Indivisible Goods
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 all agents in each group must agree that their group’s share is fair. Under this strict requirement, fair allocations exist only for small groups. We introd...
متن کامل