A Soluble Model for the Conflict between Lying and Truth-Telling

Lying and truth-telling are conflicting behavioral strategies that pervade much of the lives of social animals and, as such, have always been topics of interest to both biology and philosophy. This age-old conflict is linked to one of the most serious threats facing society today, viz., the collapse of trustworthy sources of information. Here, we revisit this problem in the context of the two-choice sender–receiver game: the sender tosses a coin and reports the supposed outcome to the receiver, who must guess the true outcome of the toss. For the sender, the options are to lie or tell the truth, while for the receiver, the options are to believe or disbelieve the sender’s account. We assume that social learning determines the strategy used by players and, in particular, that players tend to imitate successful individuals and thus change their strategies. Using the replicator equation formulation for infinite populations and stochastic simulations for finite populations, we find that when the sender benefits from the receiver’s failure, the outcome of the game dynamics depends strongly on the choice of initial strategies. This sensitivity to the initial conditions may reflect the unpredictability of social systems whose members have antagonistic interests.