In economics and game theory, Bayesian persuasion is a form of mechanism design. One participant (the sender) intends to persuade the other (the receiver) of a certain course of action. The sender must decide what action to take to maximize their expected utility by providing evidence to the receiver, under the assumption that the receiver will revise their belief about the state of the world using Bayes' Rule. Bayesian persuasion was introduced by Kamenica and Gentzkow. [1]
Bayesian persuation is a special case of a principal–agent problem: the principal is the sender and the agent is the receiver. It can also be seen as a communication protocol, comparable to signaling games; [2] the sender must decide what signal to reveal to the receiver to maximize their expected utility. It can also be seen as a form of cheap talk. [3]
Kamenica and Gentzkow [1] use the following example. The sender is a medicine company, and the receiver is the medical regulator. The company produces a new medicine, and needs the approval of the regulator. There are two possible states of the world: the medicine can be either "good" or "bad". The company and the regulator do not know the true state. However, the company can run an experiment and report the results to the regulator. The question is what experiment the company should run in order to get the best outcome for themselves. The assumptions are:
For example, suppose the prior probability that the medicine is good is 1/3 and that the company has a choice of three actions:
In this case, the third policy is optimal for the sender since this has the highest expected utility of the available options. Using the Bayes rule, the sender has persuaded the receiver to act in a favorable way to the sender.
The basic model has been generalized in a number of ways, including:
The applicability of the model has been assessed in a number of real-world contexts:
Algorithmic techniques have been developed to compute the optimal signalling scheme in practice. This can be found in polynomial time with respect to the number of actions and pseudo-polynomial time with respect to the number of states of the world. [3] Algorithms with lower computational complexity are also possible under stronger assumptions.
The online case, where multiple signals are sent over time, can be solved efficiently as a regret minimization problem. [17]
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