This paper studies one-sided matching with initial endowments and the social connections between participants are specifically considered (their social network). Different from the traditional setting, the matching starts with a group of initial participants, and the others need their invitation to join the matching game. Thus, the incentive compatibility (IC) notion here considers both reporting preferences and inviting others via their social connections. This is challenging because inviters and invitees might compete in the game. Besides IC, stability and optimality are two properties extensively studied in matching, but they both are incompatible with the new IC. In the new setting, compatible stability has been discussed, but no discussion about compatible optimality yet. We complete this and prove the theoretical boundaries regarding both stability and optimality in the new setting. We then propose a mechanism called Connected Trading Cycles to satisfy all the desirable properties for the first time. Unlike the previous solutions that add restrictions on participants' matching choices to achieve IC, we allow participants to choose anyone in the game, which in principle improves everyone's satisfiability in the matching. Finally, we give the first characterization of IC in the network setting to facilitate IC mechanism design.

翻译：本文研究具有初始禀赋的单边匹配问题，并特别考虑了参与者之间的社会联系（即其社交网络）。与传统设定不同，匹配游戏始于一组初始参与者，其他参与者需要获得他们的邀请才能加入。因此，这里的激励相容性（IC）概念同时涉及报告偏好和通过社会联系邀请他人。这具有挑战性，因为邀请者和被邀请者可能在游戏中存在竞争关系。除IC外，稳定性和最优性是匹配问题中被广泛研究的两个性质，但二者均与新的IC不相容。在新设定下，兼容稳定性已有讨论，但关于兼容最优性的探讨尚属空白。我们填补了这一空白，并证明了新设定下关于稳定性和最优性的理论边界。随后，我们提出了一种名为"联通交易循环"的机制，首次同时满足所有理想性质。与先前通过限制参与者匹配选择来实现IC的解决方案不同，我们允许参与者选择游戏中的任意对象，这在原则上提高了每个参与者在匹配中的满意度。最后，我们给出了网络环境下IC的首次特征刻画，以促进IC机制设计。