Rational and Boundedly Rational Behavior in Sender-receiver Games

We consider a signalling game in which a population of receivers decide on the outcome by majority rule, sender and receivers have conflicting interests, and there is uncertainty about both players types. We model players rationality along the lines of recent findings in behavioral game theory. We characterize the structure of the equilibria in the reduced game so obtained. We find that all pure strategy equilibria are consistent with successful attempts to mislead the receivers, and relate them to the message bin Laden sent on the eve of the 2004 US Presidential elections. The same result holds if we allow for some uncertainty about the sign of the correlation between the senders and the receivers payoffs.