A Dynamic Pricing Model under Duopoly Competition

We introduce and analyze a multi-period, finite horizon, no-replenishment, dynamic pricing model under duopoly competition between two retailers who sell an identical good. According to our duopoly competition model, a single consumer, whose valuation is uniformly distributed on [0,1], visits only one of the two retailers in each period. If the price posted by the retailer visited by the consumer is below his valuation, he purchases the good. Otherwise, in the next period the consumer visits the other retailer. We show that, as compared to the corresponding single store monopoly model, under our duopoly competition: (i) prices decline exponentially rather than linearly, (ii) the initial price converges to 0.543, rather than 1, and (iii) the system profit loss due to competition may be up to 29.6% of the monopolistic profit. It is also shown that the pricing policy does not change when the model is extended to N similar consumers. The model is further extended into a more general valuation distribution, into the capacitated case, both under similar and identical consumers, and into the centralized case.