From Optimization to Satisficing: Robust Screening under Distributional Ambiguity
This study investigates a robust screening problem under distributional ambiguity, where a seller is uncertain about a buyer's true valuation distribution, knowing only that it lies near a reference distribution measured by the Wasserstein metric. Traditional robust optimization (RO) approaches prioritize maximizing worst-case revenue within predefined ambiguity sets, often yielding seller-centric outcomes and reliance on precise set specifications. We propose a robust satisficing (RS) framework aimed at attaining a specified revenue target by minimizing the worst-case shortfall across all potential distributions. Our approach offers a tractable formulation and detailed characterization of optimal mechanisms using randomized pricing strategies. We also assess the out-of-sample efficacy of a simple posted pricing mechanism, finding it particularly effective with lower targets and positively skewed valuations, where smaller valuations have high probability mass. Comparing RO with RS, we find that RS consistently enhances buyer surplus when the reference distribution has an increasing hazard rate and increases out-of-sample seller revenue with positively skewed true valuations. Our analysis indicates that a target-driven RS framework enhances buyer surplus and fairness by offering more opportunities to lower-valuation buyers, potentially boosting overall revenue in scenarios with demand skewed toward these valuations. This approach offers a practical and viable modeling alternative to conventional RO methods, effectively overcoming the challenges of ambiguity set calibration while ensuring broader equitable access for diverse buyers.