Constrained Serial Rule on the Full Preference Domain

TL;DR

This paper introduces the Constrained Serial Rule, a new efficient mechanism for assigning objects to agents with arbitrary linear constraints, ensuring fairness and efficiency even with indifferences.

Contribution

It generalizes the Probabilistic Serial mechanism to handle linear constraints, maintaining fairness and efficiency through a linear programming approach.

Findings

Mechanism is computationally efficient.

Maintains constrained ordinal efficiency.

Ensures envy-freeness among agents of the same type.

Abstract

We study the problem of assigning objects to agents in the presence of arbitrary linear constraints when agents are allowed to be indifferent between objects. Our main contribution is the generalization of the (Extended) Probabilistic Serial mechanism via a new mechanism called the Constrained Serial Rule. This mechanism is computationally efficient and maintains desirable efficiency and fairness properties namely constrained ordinal efficiency and envy-freeness among agents of the same type. Our mechanism is based on a linear programming approach that accounts for all constraints and provides a re-interpretation of the bottleneck set of agents that form a crucial part of the Extended Probabilistic Serial mechanism.