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The existing network attack and defense method can be regarded as game, but most of the game only involves network domain, not multiple domain cyberspace. To address this challenge, this paper proposed a multiple domain cyberspace attack and defense game model based on reinforcement learning. We define the multiple domain cyberspace include physical domain, network domain and digital domain. By establishing two agents, representing the attacker and the defender respectively, defender will select the multiple domain actions in the multiple domain cyberspace to obtain defender's optimal reward by reinforcement learning. In order to improve the defense ability of defender, a game model based on reward randomization reinforcement learning is proposed. When the defender takes the multiple domain defense action, the reward is randomly given and subject to linear distribution, so as to find the better defense policy and improve defense success rate. The experimental results show that the game model can effectively simulate the attack and defense state of multiple domain cyberspace, and the proposed method has a higher defense success rate than DDPG and DQN.