Robust Optimality of Bundling Goods Beyond Finite Variance

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.