We show that computing the optimal social surplus requires $\Omega(mn)$ bits of communication between the website and the bidders in a sponsored search auction with $n$ slots on the website and with tick size of $2^{-m}$ in the discrete model, even when bidders are allowed to freely communicate with each other.

翻译：我们证明，在离散模型中，即使允许竞拍者之间自由通信，对于拥有n个广告位且刻度大小为2^{-m}的赞助搜索拍卖，计算最优社会剩余仍需要网站与竞拍者之间进行Ω(mn)比特的通信。