The application of Internet of Things promotes the cooperation among firms, and it also introduces some information security issues. Due to the vulnerability of the communication network, firms need to invest in information security technologies to protect their confidential information. In this paper, considering the multiple-step propagation of a security breach in a fully connected network, an information security investment game among n firms is investigated. We make meticulous theoretic and experimental analyses on both the Nash equilibrium solution and the optimal solution. The results show that a larger network size (n) or a larger one-step propagation probability (q) has a negative effect on the Nash equilibrium investment. The optimal investment does not necessarily increase in n or q, and its variation trend depends on the concrete conditions. A compensation mechanism is proposed to encourage firms to coordinate their strategies and invest a higher amount equal to the optimal investment when they make decisions individually. At last, our model is extended by considering another direct breach probability function and another network structure, respectively. We find that a higher connection density of the network will result in a greater expected cost for each firm.

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