Robust Competitive Ratio for Deterministic Monopoly Pricing

We study deterministic monopoly pricing under partial knowledge of the market, where the seller has access only to summary statistics of the valuation distribution, such as the mean, dispersion, and maximum value. Using tools from distributionally robust optimization and max-min analysis, we evaluate pricing strategies based on their competitive ratio (CR). We characterize the worst-case market scenario consistent with the available information and provide a complete solution for minimizing the CR. Our analysis also covers optimal pricing under various measures of dispersion, including variance and fractional moments. Interestingly, we find that the worst-case market for CR coincides with that for expected revenue. Using proof techniques tailored to the CR framework, we further examine how dispersion and maximum valuation influence optimal deterministic pricing. These results offer practical guidance for setting robust prices when market information is limited.