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.
Highlights
We introduce a new class of matching mechanisms—quantile stable mechanisms—that generate stable matchings that can be seen as a compromise between sides of a two-sided market
We focus on stable matchings, that is matchings in which each agent is willing to keep all of their contracts and there are no contracts that agents would like to sign, possibly by dropping some of their current contracts
We introduce quantile stable mechanisms: a new class of matching mechanisms that generate stable matchings that can be seen as a compromise between two sides of the market, and we study their properties
Summary
In the general matching-with-contracts model, Chen et al [17] showed that the existence of quantile stable matchings is guaranteed by two properties of agents’ preferences: strong substitutes and the law of aggregate demand Hatfield and Milgrom [2] provide the endowed assignment model in which contracts are substitutes in addition to satisfying the law of aggregate demand. We have described the endowment assignment model of Hatfield and Milgrom [2] In their model, contracts are substitutes and satisfy the law of aggregate demand, but the strong substitutes condition may fail. For further analysis of the endowment assignment model, see Delacretaz et al [30])
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