Robust Monopoly Pricing With Asymmetric Information

Abstract

This study investigates a robust monopoly pricing problem, where a seller seeks to maximize expected revenue when selling a product to a buyer with limited information, specifically knowing only the mean, variance, and asymmetric information (semivariance) of the buyer’s valuation distribution. We explore both deterministic and randomized pricing strategies and evaluate their performance under these constraints. We formulate two maximin problems aimed at maximizing the worst-case expected revenues. By employing the primal-dual approach in infinite linear programming, we derive the closed-form for the optimal pricing strategies for both maximin problems. Our results show that incorporating semivariance significantly enhances the performance of pricing strategies by better capturing distributional asymmetry. Additionally, we compare the performance of deterministic and randomized pricing in various scenarios, offering valuable insights into how risk and reward can be effectively balanced. Moreover, our results on both pricing strategies provide new bounds for the value of personalized pricing. This comprehensive analysis enables a deeper understanding of semivariance information to improve decision-making and offer practical insights for managing complex pricing decisions.