Dishonest Signalling in a Variant of Pygmalion Game

We present a variation of the Pygmalion game, a signalling game played between a population of Senders and Receivers. Senders have varying quality and can attempt to send a costly signal. Not all signals are successfully delivered or observed; the probability of success increases with the signal strength. The cost of the signal increases with the signal strength and decreases with the Sender’s quality. Receivers have no information about Senders’ qualities and can only detect the strengths of signals. Nevertheless, Receivers have to decide whether to act or not and the Receivers’ payoff is higher if they act to Senders of higher qualities. The Senders’ payoff is 1 if Receivers do act and 0 otherwise. We analyse this game and show two kinds of Nash equilibria: (1) Senders do not signal and Receivers always act and (2) all Senders send the same and relatively strong signals and Receivers always act to those signals. Thus, in Nash equilibria, only dishonest signalling occurs. Interestingly, despite the dishonesty, signalling equilibria provide some benefit to Receivers—they face a higher proportion of high-quality Senders than in the non-signalling Nash equilibrium.