Hybrid Mechanisms: Trading off Efficiency and Strategyproofness in One-Sided Matching

We study one-sided matching mechanisms where agents have vNM utility functions and report ordinal preferences. Strong impossibility results restrict the design space of strategyproof mechanisms in this domain. Improving on efficiency beyond the ex-post efficiency of Random Serial Dictatorship (RSD) generally requires trade-offs. In this paper, we introduce hybrid mechanisms, which are convex combinations of existing mechanism, and we show that they are a powerful yet simple method for trading off strategyproofness and efficiency. We present conditions under which hybrid mechanisms remain partially strategyproof with respect to a given bound for the degree of strategyproofness. At the same time, these hybrids have better efficiency properties than the less efficient component. Our approach can be successfully applied to create hybrids of RSD and the Probabilistic Serial mechanism (PS), as well as hybrids of RSD and the adaptive Boston mechanism (ABM). We provide numerical results demonstrating that the improvements can be significant.