On Solutions for the Maximum Revenue Multi-item Auction under Dominant-Strategy and Bayesian Implementations

Very few exact solutions are known for the monopolist’s k-item n-buyer maximum revenue problem with additive valuation in which k, n > 1 and the buyers i have independent private distributions F j i on items j. In this paper we derive exact formulas for the maximum revenue when k = 2 and F j i are any IID distributions on support of size 2, for both the dominant-strategy (DIC) and the Bayesian (BIC) implementations. The formulas lead to the simple characterization that, the two implementations have identical maximum revenue if and only if selling-separately is optimal for the distribution. Our results also give the first demonstration, in this setting, of revenue gaps between the two implementations. For instance, if k = n = 2 and Pr{XF = 1} = Pr{XF = 2} = 1 2 , then the maximum revenue in the Bayesian implementation exceeds that in the dominant-strategy by exactly 2%; the same gap exists for the continuous uniform distribution XF over [a, a+ 1] ∪ [2a, 2a+ 1] for all large a. Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing. This work was supported in part by the Danish National Research Foundation and the National Natural Science Foundation of China (under grant NSFC 61361136003). 1