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 weak budget balance, individual rationality, incentive compatibility, efficiency, and other properties. For example, we present sufficient conditions for mechanisms to be efficient 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 efficient mechanisms to satisfy incentive compatibility as much as possible, and incentive compatibility mechanisms to maximize the revenue. Our results provide insights into understanding auctions in social networks.

翻译：随着社交网络的发展，通过社交网络推广产品已成为一个重要问题。在社交网络拍卖中，物品需要出售给网络中的代理人，每个代理人既可以出价，也可以将销售信息传播给其邻居。因此，代理人的社会关系与其出价在拍卖中相互交织。在网络拍卖中，经典的VCG机制无法保留关键属性。为了更好地理解网络拍卖，本文针对单一物品场景，从弱预算平衡、个体理性、激励相容性、效率等性质出发，对网络拍卖进行特征描述。例如，我们提出了机制实现高效且（弱）激励相容的充分条件。借助这些性质以及奖励、参与奖励等新概念，我们展示了如何设计尽可能满足激励相容的高效机制，以及最大化收益的激励相容机制。我们的研究结果为理解社交网络中的拍卖提供了深刻见解。