Assuring communication integrity is a central problem in security. However, overhead costs associated with cryptographic primitives used towards this end introduce significant practical implementation challenges for resource-bounded systems, such as cyber-physical systems. For example, many control systems are built on legacy components which are computationally limited but have strict timing constraints. If integrity protection is a binary decision, it may simply be infeasible to introduce into such systems; without it, however, an adversary can forge malicious messages, which can cause significant physical or financial harm. To bridge the gap between such binary decisions, we propose a stochastic message authentication approach that can explicitly trade computational cost off for security. We introduce a formal game-theoretic framework for optimal stochastic message authentication, providing provable guarantees for resource-bounded systems based on an existing message authentication scheme. We use our framework to investigate attacker deterrence, as well as optimal stochastic message authentication when deterrence is impossible, in both short-term and long-term equilibria. Additionally, we propose two schemes for implementing stochastic message authentication in practice, one for saving computation only at the receiver and one for saving computation at both ends, and demonstrate the associated computational savings using an actual implementation.