Optimal Pricing in Markets with Nonconvex Costs

We consider a market run by an operator who seeks to satisfy a given consumer demand for a commodity by purchasing the needed amount from a group of competing suppliers with nonconvex cost functions. The operator knows the suppliers’ cost functions and announces a price/payment function for each supplier, which determines the payment to that supplier for producing different quantities. Each supplier then makes an individual decision about how much to produce, in order to maximize its own profit. The key question is how to design the price functions. To that end, we propose a new pricing scheme, which is applicable to general nonconvex costs, and allows using general parametric pricing functions. Optimizing for the quantities and the price parameters simultaneously, and the ability to use general parametric pricing functions allows our scheme to find prices that are typically economically more efficient and less discriminatory than those of the existing schemes. In addition, we supplement the proposed method with a polynomial-time approximation algorithm, which can be used to approximate the optimal quantities and prices. Our framework extends to the case of networked markets, which, to the best of our knowledge, has not been considered in previous work.