With the growth of networks, promoting products through social networks has become an important problem. For auctions in social networks, items are needed to be sold to agents in a network, where each agent can bid and also diffuse the sale information to her neighbors. Thus, the agents' social relations are intervened with their bids in the auctions. In network auctions, the classical VCG mechanism fails to retain key properties. In order to better understand network auctions, in this paper, we characterize network auctions for the single-unit setting with respect to IR, WBB, IC, SWM, and other properties. For example, we present sufficient conditions for mechanisms to be social welfare maximizing and (weakly) incentive compatible. With the help of these properties and new concepts such as rewards, participation rewards, and so on, we show how to design SWM mechanisms to satisfy IC as much as possible, and IC mechanisms to maximize the revenue. Our results provide insights into understanding auctions in social networks.

翻译：随着社交网络的蓬勃发展，通过社交网络推广产品已成为重要问题。针对社交网络中的拍卖，需要将商品出售给网络中的代理人——每位代理人既可出价，也可将销售信息传播给其邻居。因此，代理人的社交关系与其竞价行为在拍卖过程中相互交织。在网络拍卖中，经典VCG机制无法保持关键特性。为深入理解网络拍卖，本文针对单物品场景，从个体理性（IR）、弱预算平衡（WBB）、激励相容（IC）、社会福利最大化（SWM）等维度对网络拍卖进行刻画。例如，我们提出了机制实现社会福利最大化与（弱）激励相容的充分条件。借助这些性质及奖励、参与奖励等新概念，本文展示了如何设计尽可能满足激励相容的社会福利最大化机制，以及最大化收益的激励相容机制。研究成果为理解社交网络中的拍卖提供了重要洞见。