Inés Moreno de Barreda, Nuffield College Oxford University

"Persuasion without Commitment"

Abstract

In most signaling models the sender reveals his type through the signal and hence he is not able to persuade the receiver to choose a more favorable action than would occur under full information. For example in many models signaling by incumbent firms fails to lower the equilibrium rate of entry by challengers; and signaling by incumbent politicians fails to increase the equilibrium probability of re-election. This observation also holds in noisy signaling models if the sender’s payoff is linear in the receiver’s belief about his type.

However we show that when the receiver makes a binary decision, noisy signaling will have a systematic effect on the receiver’s decision-making, and the bias will be in favor of the sender’s preferred action, i.e. in equilibrium the sender persuades the receiver: incumbent firms will succeed in decreasing the probability of entry; and incumbent politicians will succeed in increasing their probability of re-election.

Our setup assumes additive cost of effort and additive symmetric noise. The receiver will set a threshold signal above which the sender’s preferred action is chosen. The sender’s distribution of signals will be skewed around that threshold, such that in equilibrium the receiver will perform the desired action more often than would occur under full information.

Our analysis of this model yields a number of other findings: (1) at the receiver's ex ante optimal threshold there is no persuasion; (2) nevertheless the receiver is strictly better off when senders cannot manipulate their signals; (3) if the senders face quadratic cost of effort, then the costs and benefits of signaling exactly cancel out.

The paper relates to the literature on Bayesian persuasion. In those models a sender can commit to a skewed signal structure to take advantage of nonlinearity of payoff in the receiver's beliefs. Our finding is that even without commitment, in our setting, the signal structure will endogenously become skewed to the advantage of the sender.

Contact person: Peter Norman Sørensen