This paper proposes a blockchain based trust management method for agents in a multi-agent system (MAS). In this work, three objectives are achieved: trust, cooperation and privacy. The trust of agents depends on the credibility of trust evaluators, which is verified using the proposed methods of trust distortion, consistency and reliability. To enhance the cooperation between agents, a tit-3-for-tat (T3FT) repeated game strategy is developed. The strategy is more forgiving than the existing tit-for-tat (TFT) strategy. It encourages cheating agents to re-establish their trust by cooperating for three consecutive rounds of play. Also, a proof-of-cooperation consensus protocol is proposed to improve agents' cooperation while creating and validating blocks. The privacy of agents is preserved in this work using the publicly verifiable secret sharing mechanism. The proposed methods are implemented using MATLAB R2018a while the MAS is simulated using Java Agent DEvelopment framework (JADE). Simulation results validate the effectiveness of the proposed work. From the simulation results, the proposed trust method outperforms an existing fuzzy logic trust method in terms of detecting the cheating behavior of agents in the system. Besides, the proposed T3FT strategy is effective as compared to the existing tit-for-2-tat and TFT strategies in the literature. Moreover, the security analysis of the proposed method is performed. The analysis shows that the proposed work is safe from bad-mouthing and on-off trust related attacks.