Is it always advantageous to add-on item recommendation service with a contingent free shipping policy in platform retailing?

The add-on item recommendation service with a contingent free shipping (CFS) policy has provided new opportunities to meet customers' needs and increase e-commerce platforms' profits. We consider a game problem of e-commerce revenue management in which an e-commerce platform determines the optimal CFS decisions (the CFS threshold and the basic shipping fee pricing) under the recommendation service. The models without and with the recommendation service are established to investigate the effects of recommendation service strength on the product relevance, the optimal CFS decisions and the optimal profits. The results demonstrate that the recommendation service is not always beneficial to the platform, and the relatively high service strength increases the consumers' shipping demand but reduces the consumers' add-on item demand. Under the same recommendation service strength, the add-on item price is always larger than the basic shipping fee. In addition, we also find that although moderate recommendation service strength will enhance the consumer's willingness to pay for add-on items, the platform still does not have the necessary incentive to introduce recommendation services. By considering the endogenous add-on item recommendation service to extend the proposed model, we further find that the e-commerce platform has the incentive to provide an add-on item recommendation service only when the CFS threshold is sufficiently high.