Strategy-proof size improvement: is it possible?

Abstract

The number of assigned agents (i.e., size) is an important parameter in object allocations.While size maximality clashes with individual rationality and strategy-proofness, it can stillbe possible to increase the size over a mechanism while keeping these properties. To pursuethis research, we devise a size comparison criterion to investigate the possibility of sizeincrease. A mechanism 𝜓 size-wise dominates another mechanism 𝜙 if the latter neverassigns more agents than the former, and at some problem, 𝜓 assigns more agents than 𝜙.We obtain arguably mild conditions for a mechanism to not be dominated size-wise by anindividually rational and strategy-proof mechanism. Moreover, whenever there are at least asmany objects as the total number of agents, we find conditions, different from those previouslymentioned, for a mechanism to not be dominated size-wise by an individually rational andgroup strategy-proof mechanism. These results have implications for deferred-acceptance,top trading cycles, efficiency-adjusted deferred-acceptance, serial dictatorship, and Bostonmechanisms.