Distribution-free pricing under uncertain circumstance

When pricing a product, the distribution of the seller’s value to the customer is typically unknown, although certain informational characteristics of the distribution, such as the mean and variance, can be estimated through investigation. Traditional pricing models, however, often rely on the assumption that the market is well-informed and that consumer behavior is predictable. In practice, these assumptions are frequently difficult to maintain. Consequently, this paper adopts uncertainty theory to address the problem of distribution-free pricing. The upper and lower bounds of the undistributed profit function are derived based on the profit maximization criterion. By optimizing the lower bound of profit, the optimal closed-form robust price is obtained, along with its worst-case performance under conditions of unknown distribution. Furthermore, the paper explores pricing implications and performance improvements under alternative information structures. Finally, numerical experiments and empirical analysis are conducted to verify the feasibility and practicality of the optimal and stable pricing solution.