  This paper studies a sale promotion mechanism design problem on a social
network, where a node (a seller) sells one item to the other nodes on the
network to maximize her revenue. However, the seller does not know other nodes
except for her neighbours and her neighbours have no incentive to promote the
sale. Hence, the goal is to design an auction mechanism such that the seller's
neighbours are incentivized to invite their neighbours to join the auction,
while the seller's revenue is guaranteed to increase. This is not achievable
with traditional mechanisms. One solution has been proposed recently by
carefully designing a reward scheme for the nodes who have invited others.
However, the solution only gives rewards to some cut-points of the network, but
cut-points rarely exist in a well-connected network, which actually
disincentivizes nodes' participation. Therefore, we propose another novel
mechanism to reward more related participants with fairer rewards, and the
seller's revenue is not reduced.
