When are efficient and fair assignment mechanisms group strategy-proof?

Abstract

In the house allocation model, the literature (Bade, 2016; Zhang, 2019) have proven impossibility theorems regarding the compatibility of efficiency, fairness, and group non-manipulability if agents' preferences are unrestricted. Since in many applications not all preferences are possible, this paper examines to what extent these theorems still hold on restricted preference domains. We find that these theorems still hold unless the domains are restricted to have a special tier structure. We present several possibility theorems when the number of objects is restricted or when preference domains are restricted. This paper clarifies how strong the existing impossibility theorems actually are. As corollaries, we clarify the group incentive properties of Random Priority and Probabilistic Serial, the two mechanisms at the center of many studies.