We study the communication complexity of incentive compatible auction-protocols between a monopolist seller and a single buyer with a combinatorial valuation function over $n$ items. Motivated by the fact that revenue-optimal auctions are randomized [Tha04,MV10,BCKW10,Pav11,HR15] (as well as by an open problem of Babaioff, Gonczarowski, and Nisan [BGN17]),we focus on the randomized communication complexity of this problem (in contrast to most prior work on deterministic communication). We design simple, incentive compatible, and revenue-optimal auction-protocols whose expected communication complexity is much (in fact infinitely) more efficient than their deterministic counterparts. We also give nearly matching lower bounds on the expected communication complexity of approximately-revenue-optimal auctions. These results follow from a simple characterization of incentive compatible auction-protocols that allows us to prove lower bounds against randomized auction-protocols. In particular, our lower bounds give the first approximation-resistant, exponential separation between communication complexity of incentivizing vs implementing a Bayesian incentive compatible social choice rule, settling an open question of Fadel and Segal [FS09].

翻译：我们研究垄断卖主和单一买主之间对美元物品具有组合性估价功能的奖励性兼容拍卖协议的通信复杂性。我们设计了简单、兼容性和收入最佳拍卖协议,其预期通信复杂性比其确定性对应方的效率高得多(事实上是无限的 ) 。我们还对约发性最佳拍卖的预期通信复杂性设定了近乎较低的限制。这些结果是简单描述激励性兼容性拍卖协议的特征,从而使我们能够证明与随机性拍卖协议相比有较低的限制。特别是,我们较低的界限为首个近似抗性、指数性分解规则提供了在Bay-Revenue-opative 拍卖中实施公开性稳定性社会分化规则(Bay-SIC)的公开性分解。