Analyzing Incentives and Fairness in Ordered Weighted Average for Facility Location Games

TL;DR

This paper analyzes the incentives and fairness of ordered weighted average mechanisms in facility location games, providing conditions for strategy-proofness and fairness criteria.

Contribution

It offers a comprehensive analysis of parameter conditions for incentive compatibility and fairness in ordered weighted average mechanisms.

Findings

Conditions for strategy-proofness are identified.

Criteria for individual and proportional fairness are established.

Analysis covers non-obvious manipulability of mechanisms.

Abstract

Facility location games provide an abstract model of mechanism design. In such games, a mechanism takes a profile of $n$ single-peaked preferences over an interval as an input and determines the location of a facility on the interval. In this paper, we restrict our attention to distance-based single-peaked preferences and focus on a well-known class of parameterized mechanisms called ordered weighted average methods, which is proposed by Yager in 1988 and contains several practical implementations such as the standard average and the Olympic average. We comprehensively analyze their performance in terms of both incentives and fairness. More specifically, we provide necessary and sufficient conditions on their parameters to achieve strategy-proofness, non-obvious manipulability, individual fair share, and proportional fairness, respectively.