The article explores how judges or arbitrators can make fair decisions over time using Nash's bargaining theory. They must allocate resources in a series of problems while following specific rules. The study shows that under certain conditions, the decisions made by the judge will eventually match the Nash solution. This applies to other bargaining solutions as well, like Kalai-Smorodinsky's and the egalitarian solution. The research provides a dynamic rationale for axiomatic bargaining theory, helping to understand how fair outcomes can be reached in ongoing negotiations.