Dynamic online and offline channel pricing for heterogeneous customers in virtual acceptance

We consider a manufacturer's dual distributions channels consisting on the one hand of a virtual (online) channel operated directly by a manufacturer and on the other hand of a real (offline) channel operated by an intermediate retailer. Customers are assumed heterogeneous in their virtual acceptance, deriving a surplus according to the channel they shop at. Assuming that customers' derived benefits are random with a known probability distribution, we obtain a probabilistic model, which is used to construct an inter-temporal model for shopping online. In addition, we suppose that the retailer uses a markup pricing strategy and has a strategic role. This results in a Stackleberg differential game where the manufacturer is leader and the retailer is a follower. The optimal policy shows that the manufacturer charges the same price across both channels. This finding is consistent with classical results in economics. However, our research goes beyond this observation and indicates that the online price, the retailer's markup and the probability to buy are affected by consumers' heterogeneity in a specific manner. Moreover, we show that while the retailer sets a price equal to the product value, the online price is lower and is equal to the product value less the guarantee provided by the manufacturer for the risk the customer take to buy online. This guarantee is not discriminating and is set to the risk of the customer with the lowest virtual acceptance. Finally, we show that the introduction of the online store is a win-win strategy; both the customers and the manufacturer are better off.