Dynamic Pricing for Substitute Products with Different Customer Choices Under Competition

A dynamic pricing game model for substitute products from two sellers with different customer choices was proposed, and potential customers were divided into three segments in the model: loyal customers to seller 1 who immediately purchase from seller 1 when they arrive, loyal customers to seller 2 who immediately purchase from seller 2 when they arrive, and customers with general preference for seller 1 and 2 who purchase from either seller with certain probabilities according to MNL model when they arrive. Then the existence of Nash equilibrium prices is proved, and a numerical experiment is developed to discuss the characteristics of Nash equilibrium prices.