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Online social networks (OSNs) suffer from forged messages. Current studies have typically been focused on the detection of forged messages and do not provide the analysis of the behaviors of message publishers and network strategies to suppress forged messages. This paper carries out the analysis by taking a game theoretic approach, where infinitely repeated games are constructed to capture the interactions between a publisher and a network administrator and suppress forged messages in OSNs. Critical conditions, under which the publisher is disincentivized to publish any forged messages, are identified in the absence and presence of misclassification on genuine messages. Closed-form expressions are established for the maximum number of forged messages that a malicious publisher could publish. Confirmed by the numerical results, the proposed infinitely repeated games reveal that forged messages can be suppressed by improving the payoffs for genuine messages, increasing the cost of bots, and/or reducing the payoffs for forged messages. The increasing detection probability of forged messages or decreasing misclassification probability of genuine messages also has a strong impact on the suppression of forged messages. [ABSTRACT FROM AUTHOR]