  Designing auctions to incentivize buyers to invite new buyers via their
social connections is a new trend in mechanism design. The challenge is that
buyers are competitors and we need to design proper incentives for them to
invite each other. For selling a single item, many interesting mechanisms have
been proposed. However, all the mechanisms require the seller or a third party
to be trustworthy to execute the mechanisms. In addition, the owner of the
mechanism will know all the connections of the network after the execution,
which poses a potential privacy issue. Hence, distributed mechanisms to avoid
the privacy issue are more appealing in practice. Therefore, in this paper, we
propose the first distributed mechanism in social networks without revealing
buyers' private connections to anyone, and it achieves complete
decentralization that does not rely on any trustworthy third party. Moreover,
the centralized reduction of our mechanism also offers a novel way to compute
players' contributions compared to the existing solutions.
