  Diffusion auction is a new model in auction design. It can incentivize the
buyers who have already joined in the auction to further diffuse the sale
information to others via social relations, whereby both the seller's revenue
and the social welfare can be improved. Diffusion auctions are essentially
non-typical multidimensional mechanism design problems and agents' social
relations are complicatedly involved with their bids. In such auctions,
incentive-compatibility (IC) means it is best for every agent to honestly
report her valuation and fully diffuse the sale information to all her
neighbors. Existing work identified some specific mechanisms for diffusion
auctions, while a general theory characterizing all incentive-compatible
diffusion auctions is still missing. In this work, we identify a sufficient and
necessary condition for all dominant-strategy incentive-compatible (DSIC)
diffusion auctions. We formulate the monotonic allocation policies in such
multidimensional problems and show that any monotonic allocation policy can be
implemented in a DSIC diffusion auction mechanism. Moreover, given any
monotonic allocation policy, we obtain the optimal payment policy to maximize
the seller's revenue.
