When should the offline retailer implement price matching?

In this paper, we develop a duopoly game using the Hotelling model, in which customers are uniformly distributed along the Hotelling line, and a brick-and-mortar retailer who sits on the left end of the line competes with an online retailer. The brick-and-mortar retailer is the Stackelberg leader facing strategic customers and the online retailer is the follower. Strategic customers may free ride on the BM retailer's service by first visiting the BM retailer and experiencing the product, but then switching to the online retailer to buy the product, if the retail price at the online retailer is sufficiently low. The conditions under which the BM retailer should or should not implement a price matching strategy are identified. If the cost of shopping online is high, the BM retailer can ignore the strategic customers’ behavior; there is no incentive to switch to buy the product online. When the customer's shopping cost is moderate, the BM retailer should implement a price matching strategy to prevent strategic customers from switching to the online retailer. When the cost of shopping online is low, the BM retailer should not try to match the price of the online retailer. We also show that the BM retailer's profit may increase, while the online retailer's profit may decrease, with the portion of strategic customers in the market, when the BM retailer implements a price matching strategy. When the fraction of strategic customers is sufficiently high, the BM retailer will not implement price matching strategy.