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

Equivalence between individual and group strategy-proofness under stability