Optimal Continuous Pricing with Strategic Consumers

An important problem in electronic commerce is that of finding optimal pricing mechanisms to sell a single item when the number of buyers is random and they arrive over time. In this paper we combine ideas from auction theory and recent work on pricing with strategic consumers to derive the optimal continuous time pricing scheme in this situation. blue Under the assumption that buyers are split among those who have a high valuation and those having a low valuation for the item, we obtain the price path maximizing the seller's revenue. This amounts to conclude that, depending on the specific instance it is optimal to either use a fixed price strategy, or to use steep markdowns by the end of the selling season. To complement this optimality result we prove that under a large family of price functions there exists equilibrium for the buyers. Finally, we derive an approach to tackle the case in which buyers' valuation follow a general distribution. The approach is based on optimal control theory and is well suited for numerical computations