When selling many goods with independent valuations, we develop a distributionally robust framework, consisting of a two-player game between seller and nature. The seller has only limited knowledge about the value distribution. The seller selects a revenue-maximizing mechanism, after which nature chooses a revenue-minimizing distribution from all distributions that comply with the limited knowledge. When the seller knows the mean and variance of valuations, bundling is known to be an asymptotically optimal deterministic mechanism, achieving a normalized revenue close to the mean. Moving beyond this variance assumption, we assume knowledge of the mean absolute deviation (MAD), accommodating more dispersion and heavy-tailed valuations with infinite variance. We show for a large range of MAD values that bundling remains optimal, but the seller can only guarantee a revenue strictly smaller than the mean. Another noteworthy finding is indifference to the order of play, as both the max-min and min-max versions of the problem yield identical values. This contrasts with deterministic mechanisms and the separate sale of goods, where the order of play significantly impacts outcomes. We further underscore the universality of the optimal bundling price by demonstrating its efficacy in optimizing not only absolute revenue but also the absolute regret and ratio objective among all bundling prices

翻译：针对具有独立估值的多商品销售问题，我们构建了一个包含卖方与自然两方博弈的分布稳健框架。卖方仅掌握有限的价值分布信息，需选择收益最大化机制；而自然则从所有符合该有限信息的分布中选取使卖方收益最小化的分布。当卖方已知估值均值与方差时，捆绑销售被证明是渐进最优的确定性机制，其标准化收益接近均值。突破方差假设限制，我们假设已知均值绝对偏差（MAD），从而能处理具有无限方差的更高散度与重尾估值。研究表明，在较大MAD值范围内，捆绑销售仍保持最优性，但卖方仅能获得严格小于均值的收益保障。另一重要发现是博弈顺序无关性：问题的极大极小与极小极大版本均收敛于相同值。这一结论与确定性机制及单独销售情形形成鲜明对比——后者中博弈顺序对结果具有显著影响。通过证明最优捆绑价格在绝对收益、绝对遗憾及比率目标三种优化准则下的有效性，我们进一步揭示了该价格的普适性。