A Note on Obvious Manipulations of Quantile Stable Mechanisms

In two-sided matching markets with contracts, quantile (or generalized median) stable mechanisms represent an interesting class that produces stable allocations which can be viewed as compromises between both sides of the market. These mechanisms balance the competing priorities of the parties while maintaining stability. This paper explores obvious manipulations of quantile stable mechanisms. Unfortunately, we get that any quantile stable mechanism different to the doctor-proposal DA is obviously manipulable. Our findings highlight the trade-offs between robustness to manipulation and other desirable properties, such as equity, in the design of stable matching mechanisms.