Bayesian Persuasion

Innovation and Economic Growth and Search and Advertising

Article Snapshot


Matthew Gentzkow and Emir Kamenica


American Economic Review, Vol. 101, No. 6, pp. 2590-2615, 2011


Persuasion is important in advertising, lobbying, and financial disclosure, and in the courts and political campaigns. Often, a sender of information seeks to influence the actions of a receiver of information. This study creates a mathematical model of persuasion.

Policy Relevance

The model helps analyze the effectiveness of persuasion in a wide range of settings.

Main Points

  • This study explores if and when a sender of information will be able to persuade the receiver of the information to take an action that benefits the sender; the sender chooses what information to convey to try to influence the receiver.
  • The sender can influence receiver’s beliefs, but not the payoff the receiver will obtain from the action; the sender cannot pay the receiver to perform the action by contract.
  • Revealing all the facts will help a sender/prosecutor if the defendant is guilty, but will hurt if the defendant is innocent; the judge acquits by default if she receives no information.
  • If a fully informed judge convicts 30% of the time, knowing that 70% of defendants are innocent, she can still be persuaded to convict 60% of defendants, even when aware that the investigation was designed to maximize convictions.
  • A sender benefits from persuasion unless the receiver takes the sender’s preferred action by default, and if there are a cluster of beliefs about the action that can induce receiver to act.
  • Using this model to analyze how to structure information will help induce effort without direct payments; paying a professor based on quality of research is unlikely to be feasible.
  • According to the model, optimal advertising convinces some that the product is not worth its price, while others reluctantly buy the product.
    • Making those who will never buy the product costs nothing, but increases the probability of more favorable reactions by others.
    • Improving the opinion of the product among those who will buy for certain generates no further sales.
  • Persuasion works in two ways:
    • One can increase the reward that a person will accrue from taking an action, or by increasing the penalty for doing something else.
    • One can change a person’s beliefs.
  • The person being persuaded may fail to account for the persuader’s motives, or be overwhelmed with information. But persuasion can occur even when the person being persuaded is rational.


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