Equivalence between individual and group strategy-proofness under stability

TL;DR

This paper explores the relationship between individual and group strategy-proofness in two-sided matching markets under stability, establishing an equivalence in one-to-one markets and characterizing compatible domains with single-peaked preferences.

Contribution

It proves an equivalence between individual and group strategy-proofness in one-to-one markets under certain conditions and characterizes domains with single-peaked preferences for stability and strategy-proofness.

Findings

Equivalence between individual and group strategy-proofness in one-to-one markets.

Characterization of domains with single-peaked preferences for stability.

The result does not extend to many-to-one matching markets.

Abstract

This paper studies the (group) strategy-proofness aspect of two-sided matching markets under stability. For a one-to-one matching market, we show an equivalence between individual and group strategy-proofness under stability. We obtain this equivalence assuming the domain satisfies a richness condition. However, the result cannot be extended to the many-to-one matching markets. We further consider a setting with single-peaked preferences and characterize all domains compatible for stability and (group) strategy-proofness.