DeepAI
Log In Sign Up

Probabilistic Serial Mechanism for Multi-Type Resource Allocation

04/25/2020
by   Xiaoxi Guo, et al.
0

In multi-type resource allocation (MTRA) problems, there are p ≥ 2 types of items, and n agents, who each demand one unit of items of each type, and have strict linear preferences over bundles consisting of one item of each type. For MTRAs with indivisible items, our first result is an impossibility theorem that is in direct contrast to the single type (p = 1) setting: No mechanism, the output of which is always decomposable into a probability distribution over discrete assignments (where no item is split between agents), can satisfy both sd-efficiency and sd-envy-freeness. To circumvent this impossibility result, we consider the natural assumption of lexicographic preference, and provide an extension of the probabilistic serial (PS), called lexicographic probabilistic serial (LexiPS).We prove that LexiPS satisfies sd-efficiency and sd-envy-freeness, retaining the desirable properties of PS. Moreover, LexiPS satisfies sd-weak-strategyproofness when agents are not allowed to misreport their importance orders. For MTRAs with divisible items, we show that the existing multi-type probabilistic serial (MPS) mechanism satisfies the stronger efficiency notion of lexi-efficiency, and is sd-envy-free under strict linear preferences, and sd-weak-strategyproof under lexicographic preferences. We also prove that MPS can be characterized both by leximin-ptimality and by item-wise ordinal fairness, and the family of eating algorithms which MPS belongs to can be characterized by no-generalized-cycle condition.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/13/2019

Multi-type Resource Allocation with Partial Preferences

We propose multi-type probabilistic serial (MPS) and multi-type random p...
09/18/2021

Favoring Eagerness for Remaining Items: Achieving Efficient and Fair Assignments

In the assignment problem, items must be assigned to agents who have uni...
01/29/2021

Sequential Mechanisms for Multi-type Resource Allocation

Several resource allocation problems involve multiple types of resources...
12/14/2019

The Crawler: Two Equivalence Results for Object (Re)allocation Problems when Preferences Are Single-peaked

For object reallocation problems, if preferences are strict but otherwis...
07/14/2020

An Axiomatic Decomposition of Strategyproofness for Ordinal Mechanism with Indifferences

We study mechanism which operate on ordinal preference information (i.e....
05/31/2017

Obtaining a Proportional Allocation by Deleting Items

We consider the following control problem on fair allocation of indivisi...
09/23/2019

On Weighted Envy-Freeness in Indivisible Item Allocation

In this paper, we introduce and analyze new envy-based fairness concepts...