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Lies can have profoundly negative consequences for individuals, groups and even for societies. Understanding how lying evolves and when it proliferates is therefore of significant importance for our personal and societal well-being. To that effect, we here study the sender–receiver game in well-mixed populations with methods of statistical physics. We use the Monte Carlo method to determine the stationary frequencies of liars and believers for four different lie types. We consider altruistic white lies that favour the receiver at a cost to the sender, black lies that favour the sender at a cost to the receiver, spiteful lies that harm both the sender and the receiver, and Pareto white lies that favour both the sender and the receiver. We find that spiteful lies give rise to trivial behaviour, where senders quickly learn that their best strategy is to send a truthful message, while receivers likewise quickly learn that their best strategy is …