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This paper proposes a multi-agent decision model based on recurrent neural networks and particle swarm optimization technology. In this paper, the recurrent neural network is used for strategy decision controller. The inputs of the recurrent neural network are decided by the last strategies of other agents. Then the outputs determine the next strategy that the agent will choose. The weight values are updated by particle swarm optimization algorithm. The multi-agent decision model is applied in public goods games, and numerical results show that this decision model has the ability of adaptive learning and can prevent the collision between agents to realize the total social utility maximum.