Secure Message Transmission (SMT) is a two-party cryptographic protocol by which the sender can securely and reliably transmit messages to the receiver using multiple channels. It is assumed that an adversary corrupts a subset of the channels, and makes eavesdropping and tampering over the corrupted channels. In this work, we consider a game-theoretic security model for SMT. Specifically, we introduce a rational adversary who has the preference for the outcome of the protocol execution. We show that, under some reasonable assumption on the adversary’s preference, even if the adversary corrupts all but one of the channels, it is possible to construct SMT protocols with perfect security against rational adversaries. More specifically, we consider “timid” adversaries who prefer to violate the security requirement of SMT, but do not prefer the tampering actions to be detected. In the traditional cryptographic setting, perfect SMT can be constructed only when the adversary corrupt a minority of the channels. Our results demonstrate a way of circumventing the impossibility results of cryptographic protocols based on a game-theoretic approach.