Probabilistic Serial Mechanism for Multi-Type Resource Allocation
Xiaoxi Guo, Sujoy Sikdar, Haibin Wang, Lirong Xia, Yongzhi Cao, Hanpin, Wang

TL;DR
This paper introduces a new mechanism called LexiPS for multi-type resource allocation with indivisible items under lexicographic preferences, overcoming an impossibility result and ensuring efficiency, envy-freeness, and strategyproofness.
Contribution
It extends the probabilistic serial mechanism to multi-type settings with indivisible items under lexicographic preferences, achieving desirable fairness and efficiency properties.
Findings
LexiPS satisfies sd-efficiency and sd-envy-freeness.
MPS satisfies lexi-efficiency and is sd-envy-free under strict preferences.
MPS characterized by leximin-ptimality and no-generalized-cycle condition.
Abstract
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…
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Taxonomy
TopicsGame Theory and Voting Systems · Constraint Satisfaction and Optimization · Logic, Reasoning, and Knowledge
