Bayesian Persuasion with Lie Detection
How does lie detection constrain the potential for one person to persuade another to change her action? We consider a model of Bayesian persuasion in which the Receiver can detect lies with positive probability. We show that the Sender lies more when the lie detection probability increases. As long as this probability is sufficiently small, the Sender's and the Receiver's equilibrium payoffs are unaffected by the presence of lie detection because the Sender simply compensates by lying more. However, when the lie detection probability is sufficiently high, the Sender's equilibrium payoff decreases and the Receiver's equilibrium payoff increases with the lie detection probability.
We are particularly grateful to Andrew Little for inspiring our initial analysis. We also thank Joshua Gans, Scott Gehlbach, Matt Gentzkow, Philippe Jehiel, Navin Kartik, Kohei Kawamura, Elliot Lipnowski, Zhaotian Luo, Barry Nalebuff, Jacopo Perego, Larry Samuelson, Julia Simon-Kerr, Joel Sobel, and Ian Turner for helpful comments. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.