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.

我认为住房市场问题的偏好较弱。在这种情况下，我为弱势群体战略证明提供了充分条件；没有一组代理商可以共同地误报其偏好，从而使该组中的每个代理商变得更好。使用此充分条件，我证明了最高交易吸收集，最高周期和最高优先级对象规则满足弱组策略证明。因此，本文建立，这是可能实现弱势群体战略proofness，与其他理想的结果一起，为住房市场的问题与薄弱的喜好，即使组策略proofness是不兼容在这种情况下的帕累托效率。