[Paper Review] Partially Strategyproof Mechanisms for the Assignment Problem

Timo Mennle, Sven Seuken|arXiv (Cornell University)|Mar 11, 2013

Game Theory and Voting Systems20 references4 citations

TL;DR

This paper introduces partially strategyproof mechanisms for the assignment problem, analyzing manipulability and efficiency through dominance relations between mechanisms. It establishes that if mechanism g imperfectly dominates f, then the convex combination hβ(f,g) also imperfectly dominates f, forming a hierarchy of manipulability and efficiency.

ABSTRACT

• Prop. 8. If g imperfectly dominates f, then hβ(f,g) imperfectly dominates f. ... and yield a hierarchy of manipulability and efficiency. • Prop. 9./10. Given f SP, g manipulable and weakly less varying than f, g imperfectly dominates f, 0≤β 0:

Motivation & Objective

• To develop mechanisms that are partially strategyproof in the assignment problem.
• To analyze the trade-off between manipulability and efficiency in mechanism design.
• To formalize a hierarchy of mechanisms based on imperfect dominance relations.
• To characterize conditions under which one mechanism weakly dominates another in terms of manipulability and efficiency.

Proposed method

• Uses the concept of imperfect dominance to compare mechanisms f and g.
• Applies convex combinations hβ(f,g) = (1−β)f + βg to generate new mechanisms.
• Analyzes how dominance relations are preserved under convex combinations.
• Employs the condition that g is weakly less varying than f to ensure dominance.
• Establishes theoretical results using properties of strategyproofness and variation in mechanisms.
• Relies on propositions to derive structural relationships between mechanisms.

Experimental results

Research questions

• RQ1 Under what conditions does a mechanism g imperfectly dominate another mechanism f?
• RQ2 How does convex combination hβ(f,g) affect the dominance and strategyproofness properties of f and g?
• RQ3 What is the role of variation in mechanisms in determining dominance relations?
• RQ4 Can a hierarchy of manipulability and efficiency be systematically constructed from dominance relations?
• RQ5 How does weakly less variation in g relative to f influence the dominance outcome?

Key findings

• If g imperfectly dominates f, then the convex combination hβ(f,g) also imperfectly dominates f for all β in [0,1].
• When f is strategyproof and g is manipulable but weakly less varying than f, g imperfectly dominates f.
• The hierarchy of mechanisms is preserved under convex combinations, maintaining the dominance structure.
• Imperfect dominance provides a formal framework to compare mechanisms in terms of manipulability and efficiency.
• The results establish a theoretical foundation for constructing mechanisms that balance strategyproofness and efficiency.
• The dominance relations are robust under convex combinations, enabling systematic mechanism design.