Truncation-Invariant Allocation

Abstract

We consider an abstract allocation model that includes an initial state over which agents have private preferences. Agents' preferences can be strict or weak, and externalities can exist or not. A deterministic mechanism finds an allocation whereas a random mechanism finds a probability distribution over allocations. We say a mechanism, either deterministic or random, is truncation-invariant if after an agent truncates preferences, the found allocation is invariant in some respect as defined in the paper. Truncation-invariance is weaker than strategy-proofness and satisfied by some well-known manipulable mechanisms. For individually rational and truncation-invariant mechanisms, we prove two theorems that provide a unified explanation of seemingly unrelated results in several distinct models, which include object allocation, matching with contracts, and the abstract models of Sonmez (1999) and Alva and Manjunath (2019). The two theorems are straightforwardly implied by the definition of truncation-invariance, yet they are surprisingly useful in understanding existing results.