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The Industrial Internet of Things (IIoT) network is composed of devices that contain sensitive data, which makes them vulnerable to various security threats. Digital Certificates can be used to reinforce the security of the IIoT network, however, their management remains a major issue. Hence, in this article, we rely on trust management to deal with the whole certificate management process in IIoT networks, from revocation to verification. For this purpose, we organize the IIoT network into a clustering architecture where each cluster head (CH) hosts an agent, called CH-UR agent, that renews/revokes the certificates of its cluster member nodes. We apply signaling game theory to build a Certificate Revocation Game modeling the interactions between a member IIoT node and the CH-UR agent. Thus, upon the belief on the member node, updated by using the Bayesian rules, the best response strategy for the CH-UR …