We study the classic house-swapping problem of Shapley and Scarf (1974) in a setting where agents may have "objective" indifferences, i.e., indifferences that are shared by all agents. In other words, if any one agent is indifferent between two houses, then all agents are indifferent between those two houses. The most direct interpretation is the presence of multiple copies of the same object. Our setting is a special case of the house-swapping problem with general indifferences. We derive a simple, easily interpretable algorithm that produces the unique strict core allocation of the house-swapping market, if it exists. Our algorithm runs in square polynomial time, a substantial improvement over the cubed time methods for the more general problem.

翻译：我们研究Shapley和Scarf（1974）提出的经典房屋交换问题，其中的参与者可能具有“客观”无差异偏好，即所有参与者共享的无差异偏好。换言之，若任何一位参与者对两套房屋无差异，则所有参与者对这两套房屋均无差异。最直接的解释是同一物品存在多个副本。我们的设定是一般无差异房屋交换问题的特例。我们推导出一个简单且易于解释的算法，该算法能产生房屋交换市场的唯一严格核配置（若存在）。该算法运行时间为平方多项式时间，相较于解决更一般问题的立方时间方法有了显著改进。