This paper studies a house allocation problem in a networked housing market, where agents can invite others to join the system in order to enrich their options. Top Trading Cycle is a well-known matching mechanism that achieves a set of desirable properties in a market without invitations. However, under a tree-structured networked market, existing agents have to strategically propagate the barter market as their invitees may compete in the same house with them. Our impossibility result shows that TTC cannot work properly in a networked housing market. Hence, we characterize the possible competitions between inviters and invitees, which lead agents to fail to refer others truthfully (strategy-proof). We then present a novel mechanism based on TTC, avoiding the aforementioned competition to ensure all agents report preference and propagate the barter market truthfully. Unlike the existing mechanisms, the agents' preferences are less restricted under our mechanism. Furthermore, we show by simulations that our mechanism outperforms the existing matching mechanisms in terms of the number of swaps and agents' satisfaction.

翻译：本文研究网络化住房市场中的房屋分配问题，其中代理人可邀请他人加入系统以丰富其可选资源。在无邀请机制的市场中，顶级交易循环（TTC）是一种广为人知的匹配机制，能够实现一组理想性质。然而，在树状结构的网络化市场中，现有代理人必须策略性地推广易货市场，因为其邀请者可能与他们竞争同一套房屋。我们的不可能性结果表明，TTC无法在网络化住房市场中正常工作。因此，我们刻画了邀请者与被邀请者之间可能存在的竞争关系，这种竞争导致代理人无法真实地推荐他人（即防策略性失效）。进而，我们提出了一种基于TTC的新机制，避免了上述竞争，从而确保所有代理人如实报告偏好并真实地传播易货市场。与现有机制相比，本机制对代理人偏好的限制更少。此外，模拟实验表明，本机制在交换次数和代理人满意度方面均优于现有匹配机制。