Group incentive compatibility in the housing market problem with weak preferences

Abstract

I consider the housing market problem with weak preferences. In this context, I provide a sufficient condition for weak group strategy proofness; no group of agents can jointly misreport their preferences such that each agent in the group becomes better-off. Using this sufficient condition, I prove that the top trading absorbing sets, top cycles, and highest priority object rules satisfy weak group strategy proofness. Thus, this paper establishes that it is possible to achieve weak group strategy proofness, along with other desirable results, for the housing market problem with weak preferences even though group strategy proofness is incompatible with Pareto efficiency in this setting.