Dynamic pricing for group-buying strategy with network externality

We consider a two-stage dynamic pricing problem for a seller who employs online group purchasing with strategic customers. Customers who arrive in Periods 1 and 2 can decide whether to purchase the product in the current period, delay their purchases to the next period (for those customers in Period 1), or leave the market. The network externality, a typical characteristic of group buying, is captured in our model. That is, more customers who purchase the product would positively or negatively affect the demand. We investigate the impacts of positive/negative externality on the seller's prices, demands, and profits, respectively. By comparing positive and negative externality cases, we find that customers who purchase the product in Period 2 can enjoy a lower price than in Period 1 for negative externality. Interestingly, however, the price in Period 1 might be higher or lower than in Period 2 for positive externality, even if the corresponding demand is lower. Compared to no externality, our result shows that the seller should reduce the price in Period 1 but increase it in Period 2 because this helps increase the total demand and profit in the presence of a positive externality. Nevertheless, when there exists a negative externality, we confirm that the prices in two periods might both decrease for a lower externality, which leads to lower total demand and profit for the seller. Since the seller can decide whether to disclose their reviews or product historical sales to customers, this result can provide practical implications for sellers who adopt a group purchasing strategy.