In the context of the Belt and Road Initiative (BRI), demand in informatization and coordinated logistics services is playing increasing attention to the frequent international trade transactions. Several authors have proposed models about supply chain information sharing focused on product supply chain to analyze the factors affecting the level of corporate information sharing and the relationship between the level of information sharing and corporate performance, etc. However, little is available to study on the decision-making issues of corporate information sharing in the service supply chain. This paper aims to reveal the possible impact of the government's infrastructure construction investment and government incentives on the logistics service supply chain in the logistics service supply chain under this theme. This paper constructs an evolutionary game model to explore the dynamic selection process of corporate information co-strategy, the logistics service supply chain composed of functional logistics service provider (FLSP) and logistics service integrator (LSI) taked as the research object. Numerical experiments show that the additional revenue of information sharing, revenue distributing coefficient, information sharing risk coefficient and the speculative income coefficient are closely to the probability of gamers' choosing information sharing; moreover, investment in government infrastructure construction is conducive to improving the initial willingness of logistics companies to implement information sharing in which the government's incentives for corporate information sharing behavior are directly proportional to the probability of logistics companies choosing information sharing. We discuss the practical implications of the proposed model, and the wider implications for improving the level of international logistics cooperation and the high-quality development of logistics enterprise informatization under the BRI.