  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.
