E-commerce firms such as JD.com have launched logistics sharing alliance (LSA) by providing logistics services to the society. However, should their rivals having logistics service disadvantages join the LSA? In this paper, we formulate competing e-commerce firms' incentives regarding logistics cooperation via LSA. Firm A (she) offers LSA. Firm B (he) may guarantee customers a promised delivery time (PDT), although he has logistics services disadvantages. Without PDT, we find that firm B's profit performance joining LSA will be hurt when the market competition intensity degree is either high or low. We characterize firm B's total sales and the allocation ratio because of firm A's logistics sharing to explain this interesting finding. In contrast, when firm B has PDT guarantee, we find that he will join LSA when the PDT cost is high and the competition intensity degree is low. That is, PDT increases firm B's incentives to join LSA when he faces mild competition from firm A.