Abstract
We construct quantile stable mechanisms, show that they are distinct in sufficiently large markets, and analyze how they can be manipulated by market participants. As a step to showing that quantile stable mechanisms are well defined, we show that median and quantile stable matchings exist when contracts are strong substitutes and satisfy the law of aggregate demand. This last result is of independent interest as experiments show that agents who match in a decentralized way tend to coordinate on the median stable matching when it exists.
Chen, Peter