In an influential paper, Grafen (1990) provided a mathematical demonstration of the validity of Zahavi's handicap principle . Grafen showed how an honest signalling system is stabilized through costly signalling: cost stabilizes the system when the cost of lying is greater than any benefit associated with doing so. Because cost serves to prevent lies, a stable signalling system clearly will require some sort of cost associated with lying. Must there be cost associated with telling the truth, as well? In Grafen's model, the answer is ``yes''. Subsequent discrete models (models that allow only a finite set of discrete states and a finite set of discrete signals) yield the opposite result: cost need not be associated with honest signals, so long as dishonest signals are costly. In this letter we show that this an artifact of the discrete nature of these models. In continuous models, even if different signallers have distinct 'optimal' characters, when these characters are used as signals, the system will go to an equilibrium at which signalling is costly.
