A claim can be understood as a negative result of the performance of a contract, as it is necessary to fulfill the obligation and/or indemnify (freight damage claim, for example). Today’s claims management faces a variety of problems, such as inefficient claims postings, possible data forgery, and a very lengthy claims resolution process. All these problems can be solved by using a synthesis of innovative tools, e.g., a blockchain system, game theory, and statistical methods. Theoretical possibilities and practical examples regarding solving claims management problems were identified by analyzing various scientific sources. However, it remained unclear whether these methods could interact with each other, complicate the existing claims settlement process or not, or whether a synthesis of such measures would be viable. Therefore, a qualitative study was conducted and answers to the above questions were found. The research revealed that 75% of international Lithuanian logistics companies can apply the synthesis of these methods in claims management and solutions. Using the concordance coefficient formula, the value of W was calculated. This coefficient indicated that the opinions of the experts who participated in the study were somewhat similar. The value of the actual χ2 distribution was also calculated. The result obtained shows that the experts’ opinions were somewhat harmonized and that their compatibility was not accidental. The use of blockchain system synthesis in combination with game theory and statistical methods could help international logistics companies to reduce their costs, speed up the management process, and increase data security and reliability while ensuring structured one-stop claims management.