A Continuous-Time Dynamic Pricing Model Knowing the Competitor’s Pricing Strategy

TLDR: In this article, the authors consider a dynamic pricing model for a firm knowing that a competitor adopts a static pricing strategy and establish a continuous time model to analyze the effect of the dynamic pricing on the improvement of revenue in the duopoly market.

Abstract: In this paper the authors consider a dynamic pricing model for a firm knowing that a competitor adopts a static pricing strategy. The authors establish a continuous time model to analyze the effect of the dynamic pricing on the improvement of revenue in the duopoly market. Suppose that customers arrive to purchase tickets in accordance with a geometric Brownian motion. The authors derive an explicit closed-form expression for optimal pricing policy to maximize the expected revenue. It is shown that when the competitor adopts a flat rate pricing policy, a dynamic pricing is not always effective in terms of the expected revenue compared to the fixed pricing strategy. Moreover, the authors show that the size of reduction for expected revenue depends on the competitor’s pricing strategy. Numerical results are presented to illustrate the dynamic pricing policy.