Abstract We study the house allocation problem with existing tenants: n houses (stand for “indivisible objects”) are to be allocated to n agents; each agent needs exactly one house and has strict preferences; k houses are initially unowned; k agents initially do not own houses; the remaining n − k agents (the so-called “existing tenants”) initially own the remaining n − k houses (each owns one). In this setting, we consider various randomized allocation rules under which voluntary participation of existing tenants is assured and the randomization procedure either treats agents equally or discriminates against some (or all) of the existing tenants. We obtain two equivalence results, which generalize the equivalence results in Abdulkadiroglu and Sonmez (1999) and Sonmez and Unver (2005).

中文翻译：

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现有租户的房屋分配随机机制

摘要 我们研究现有租户的房屋分配问题：n 个房屋（代表“不可分割的对象”）分配给 n 个代理；每个代理商只需要一所房子，并且有严格的偏好；k 房子最初是无主的；k 代理最初不拥有房屋；剩余的 n - k 个代理（所谓的“现有租户”）最初拥有剩余的 n - k 个房屋（每个人拥有一个）。在这种情况下，我们考虑各种随机分配规则，在这些规则下，现有租户的自愿参与得到保证，随机化程序要么平等对待代理，要么歧视部分（或全部）现有租户。我们获得了两个等价结果，它们概括了 Abdulkadiroglu 和 Sonmez (1999) 以及 Sonmez 和 Unver (2005) 中的等价结果。