Blockchain technology has attracted widespread attention due to its advantages of decentralization, as well as non-tampering, transparency, and traceability of information. Fourth-party logistics systems that do not use blockchain incur transaction costs and service quality losses due to the inability to fully control the delivery process, whereas the use of blockchain eliminates the transaction costs and quality losses, but the use of blockchain needs implementation and marginal use costs. To study the conditions for the use of blockchain technology, consider the fourth-party logistics system does not use and uses blockchain technology, and the equilibrium strategies in the two cases are compared. Numerical experiments show that there exists a certain range of blockchain costs which leads to a Pareto improvement in profits for both fourth-party logistics and third-party logistics and an improvement in the quality of logistics services when using blockchain.