  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 favor the receiver
at a cost to the sender, black lies that favor the sender at a cost to the
receiver, spiteful lies that harm both the sender and the receiver, and Pareto
white lies that favor both the sender and the receiver. We find that spiteful
lies give rise to trivial behavior, where senders quickly learn that their best
strategy is to send a truthful message, whilst receivers likewise quickly learn
that their best strategy is to believe the sender's message. For altruistic
white lies and black lies, we find that most senders lie while most receivers
do not believe the sender's message, but the exact frequencies of liars and
non-believers depend significantly on the payoffs, and they also evolve
non-monotonically before reaching the stationary state. Lastly, for Pareto
white lies we observe the most complex dynamics, with the possibility of both
lying and believing evolving with all frequencies between 0 and 1 in dependence
on the payoffs. We discuss the implications of these results for moral behavior
in human experiments.
