Most market mechanisms that we encounter in practice aren't strategy proof, and many markets don't admit any strategyproof mechanisms, so we need to have a language to talk about how strategyproof a mechanism is or isn't. There are a number of approaches to that, and here's a new one.
Partial strategyproofness: Relaxing strategyproofness for the random assignment problem
Timo Mennle and Sven Seuken, Journal of Economic Theory, Volume 191, January 2021
Abstract: We present partial strategyproofness, a new, relaxed notion of strategyproofness for studying the incentive properties of non-strategyproof assignment mechanisms. Informally, a mechanism is partially strategyproof if it makes truthful reporting a dominant strategy for those agents whose preference intensities differ sufficiently between any two objects. We demonstrate that partial strategyproofness is axiomatically motivated and yields a parametric measure for “how strategyproof” an assignment mechanism is. We apply this new concept to derive novel insights about the incentive properties of the probabilistic serial mechanism and different variants of the Boston mechanism.
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