We study a class of priority-based allocation problems, the general job rotation problems first proposed by Yu and Zhang (2020), in which each position is occupied by at most one agent, and each agent occupies at most one position. The priority structure is that at each occupied position, its occupant has the lowest priority while all other agents have equal highest priority; at other positions, all agents have equal priority. This priority structure is the “opposite” to that in house allocation with existing tenants (HET) problem proposed by Abdulkadiroğlu and Sönmez (1999). We propose two constrained efficient mechanisms: one is the mechanism, the other is the mechanism. Both of the two mechanisms are adapted from mechanisms in the HET model. In a special setup that there are equal numbers of agents and positions, each agent occupies exactly one position, and all positions are acceptable for all agents, these two mechanisms yield the same outcome, which is also the outcome of the mechanism proposed by Yu and Zhang (2020). In such a setup, our two mechanisms are also weakly group strategy-proof.

中文翻译：

---

论岗位轮换问题的两种机制

我们研究一类基于优先级的分配问题，即Yu和Zhang（2020）首先提出的一般工作轮换问题，其中每个职位最多由一个代理人占据，每个代理人最多占据一个职位。优先级结构是，在每个占用位置，其占用者具有最低优先级，而所有其他代理具有相同的最高优先级；在其他职位上，所有代理具有同等优先权。这种优先结构与 Abdulkadiroğlu 和 Sönmez (1999) 提出的现有租户住房分配 (HET) 问题“相反”。我们提出两种约束有效机制：一是机制，二是机制。这两种机制均改编自 HET 模型中的机制。在一种特殊的设置中，即代理数量和位置相等，每个代理恰好占据一个位置，并且所有位置对于所有代理来说都是可接受的，这两种机制产生相同的结果，这也是Yu和Yu提出的机制的结果张（2020）。在这样的设置中，我们的两种机制也具有弱的群体策略证明。