The main goal of this paper is to investigate continuous-time distributed dynamic programming (DP) algorithms for networked multi-agent Markov decision problems (MAMDPs). In our study, we adopt a distributed multi-agent framework where individual agents have access only to their own rewards, lacking insights into the rewards of other agents. Moreover, each agent has the ability to share its parameters with neighboring agents through a communication network, represented by a graph. We first introduce a novel distributed DP, inspired by the distributed optimization method of Wang and Elia. Next, a new distributed DP is introduced through a decoupling process. The convergence of the DP algorithms is proved through systems and control perspectives. The study in this paper sets the stage for new distributed temporal different learning algorithms.

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