Interacting competitively requires vigilance to avoid deception. However, excessive caution can have adverse effects, stemming from false beliefs of intentional harm. So far there is no formal cognitive account of what may cause this suspiciousness. Here we present an examination of this phenomenon through the lens of Theory of Mind - the cognitive ability to consider the beliefs, intentions, and desires of others. By simulating interacting computer agents we illustrate how well-aligned agents can give rise to successful deception and justified skepticism. Crucially, we also reveal that overly cautious agents develop false beliefs that an ingenuous partner is attempting malicious trickery, leading to tangible losses. As well as formally defining a plausible mechanism for suspiciousness, paranoia, and conspiratorial thinking, our theory indicates that rather than a deficit in Theory of Mind, paranoia may involve an over-application of strategy to genuine behaviour.