Rational and Boundedly Rational Behavior in a Binary Choice Sender–Receiver Game

The authors investigate the strategic rationale behind the message sent by Osama bin Laden on the eve of the 2004 U.S. Presidential elections. They model this situation as a signaling game in which a population of receivers takes a binary choice, the outcome is decided by majority rule, sender and receivers have conflicting interests, and there is uncertainty about both players' degree of rationality. They characterize the structure of the sequential equilibria of the game as a function of the parameters governing the uncertainty and find that in all pure strategy equilibria, the outcome most preferred by the rational sender is chosen. An explanation of the above-mentioned events relies crucially on the relative likelihood of rational and naive players: If a sufficient departure from full rationality of the electorate is posited, then our model suggests that bin Laden's pre-electoral message succeeded in tilting the race toward his preferred outcome.