On Truthful Mechanisms for Maximin Share Allocations
نویسندگان
چکیده
We study a fair division problem with indivisible items, namely the computation of maximin share allocations. Given a set of n players, the maximin share of a single player is the best she can guarantee to herself, if she would partition the items in any way she prefers, into n bundles, and then receive her least desirable bundle. The objective then is to find an allocation, so that each player is guaranteed her maximin share. Previous works have studied this problemmostly algorithmically, providing constant factor approximation algorithms. In this work we embark on amechanism design approach and investigate the existence of truthful mechanisms. We propose three models regarding the information that the mechanism attempts to elicit from the players, based on the cardinal and ordinal representation of preferences. We establish positive and negative (impossibility) results for each model and highlight the limitations imposed by truthfulness on the approximability of the problem. Finally, we pay particular attention to the case of two players, which already leads to challenging questions.
منابع مشابه
Groupwise Maximin Fair Allocation of Indivisible Goods
We study the problem of allocating indivisible goods among n agents in a fair manner. For this problem, maximin share (MMS) is a well-studied solution concept which provides a fairness threshold. Specifically, maximin share is defined as the minimum utility that an agent can guarantee for herself when asked to partition the set of goods into n bundles such that the remaining (n− 1) agents pick ...
متن کاملOn Low-Envy Truthful Allocations
We study the problem of allocating a set of indivisible items to players having additive utility functions over the items. We consider allocations in which no player envies the bundle of items allocated to the other players too much. We present a simple proof that deterministic truthful allocations do not minimize envy by characterizing the truthful mechanisms for two players and two items. Als...
متن کاملX Fair Enough: Guaranteeing Approximate Maximin Shares
We consider the problem of fairly allocating indivisible goods, focusing on a recently-introduced notion of fairness called maximin share guarantee: Each player’s value for his allocation should be at least as high as what he can guarantee by dividing the items into as many bundles as there are players and receiving his least desirable bundle. Assuming additive valuation functions, we show that...
متن کاملApproximate Maximin Share Allocations in Matroids
The maximin share guarantee is, in the context of allocating indivisible goods to a set of agents, a recent fairness criterion. A solution achieving a constant approximation of this guarantee always exists and can be computed in polynomial time. We extend the problem to the case where the goods collectively received by the agents satisfy a matroidal constraint. Polynomial approximation algorith...
متن کاملOn Worst-Case Allocations in the Presence of Indivisible Goods
We study a fair division problem, where a set of indivisible goods is to be allocated to a set of n agents. Each agent may have different preferences, represented by a valuation function that is a probability distribution on the set of goods. In the continuous case, where goods are infinitely divisible, it is well known that proportional allocations always exist, i.e., allocations where every a...
متن کامل