Multi-agent systems (MAS) are one of the prominent symbols of artificial intelligence (AI) that, in spite of having smaller entities as agents, have many applications in software development, complex system modeling, intelligent traffic control, etc. Learning of MAS, which is commonly based on Reinforcement Learning (RL), is one of the problems that play an essential role in the performance of such systems in an unknown environment. A major challenge in Multi-Agent Reinforcement Learning (MARL) is the problem of credit assignment in them. In this paper, in order to solve Multi-agent Credit Assignment (MCA) problem, we present a bottom-up method based on the bankruptcy concept for the effective distribution of the credits received from the environment in a MAS so that its performance is increased. In this work, considering the Task Start Threshold (TST) of the agents as a new constraint and a multi-score environment, as well as giving priority to agents of lower TST, three methods PTST, T-MAS and T-KAg are presented, which are based on the bankruptcy concept as a sub branch of game theory. In order to evaluate these methods, seven criteria were used among which density was a new one. The simulation results of the proposed methods indicated that the performance of the proposed methods was enhanced in comparison with those of the existing methods in six parameters while it proved a weaker performance in only one parameter.