Cheap talk vs Bayesian persuasion: when should you trust a strategic message?

Cheap talk is costless communication with strategic incentives

In a cheap-talk model, the message itself does not directly change payoffs or bind the sender to an action. That does not mean every message is a lie or that communication is always useless. The receiver considers what the sender knows and which response the sender prefers. The extent of preference alignment affects what can be communicated credibly in a specified game.

Use the cheap-talk game to compare an aligned truthful script with a sender that always recommends the high action. Crawford and Sobel’s original paper develops strategic information transmission more generally. Modic’s scripted comparison does not compute all equilibria of that model. Its narrower purpose is to make you ask whether a message distinguishes states that matter to the receiver.

Bayesian persuasion changes the experiment behind the message

Information design gives a sender a different power: choosing a signal rule before the state is drawn or revealed under the model’s commitment structure. The receiver knows the rule and updates from the signal. A persuasive positive signal can be credible precisely because its rate of appearing in each state is disclosed. The sender cannot freely rewrite the rule after seeing an inconvenient outcome.

In the Bayesian-persuasion simulation, the prior probability of a good state is 0.3. Good states always receive a positive signal; the adjustable parameter is how often bad states also do. Kamenica and Gentzkow’s paper provides the primary framework. The teaching objective is a transparent posterior calculation under a deliberately small game, not a universal recipe for marketing or political influence.

Worked example: make a positive signal just persuasive enough

These probabilities define the toy game. The receiver invests at a posterior of at least one-half, including the exact tie; changing that tie rule changes the boundary outcome.

1. Set the bad-state positive rate to zero. A positive signal then comes only from good states. Its probability is 0.3 and the receiver’s posterior after a positive signal is one.
2. Raise that rate to 3/7 using the boundary preset. Positive signals now occur with probability 0.3 + 0.7 × 3/7 = 0.6. The good-state share of positive signals is 0.3 / 0.6 = 0.5.
3. Increase the rate beyond 3/7. Positive signals become more frequent, but their posterior drops below one-half and the receiver rejects them under the stated rule. More optimistic messages can therefore produce less investment in this particular game.

Correlated equilibrium asks whether following advice is worthwhile

The correlated-equilibrium traffic game uses a shared device to coordinate two players in a small Chicken payoff matrix. Opposite recommendations avoid a collision in the scripted play. The relevant incentive question is conditional: after receiving your recommendation, would changing your own action improve your expected payoff while the other player follows theirs?

Coordination does not require both players to receive the same instruction. Nor does a shared random number automatically create a correlated equilibrium for any payoff table. Inspect the actual rewards, the recommendation distribution and what each player learns. The displayed device illustrates one incentive-compatible construction; it does not establish that an unannounced human convention will work or that every player will obey a recommendation.

An information-and-incentives checklist

Apply this before deciding whether a strategic message deserves weight. It works best when the answers are concrete enough that someone else can inspect them.

• State what the sender observes before speaking, which actions are available and how the sender’s payoff changes with your response.
• Ask whether the signal rule is fixed in advance and visible to the receiver. Distinguish a disclosed testing process from a claim that an undisclosed process was fair.
• Update using the probability of the message in every relevant state. The frequency of positive messages is not itself the probability that a positive message is correct.
• Check the receiver’s threshold and tie convention, then test the incentive to deviate after each recommendation rather than checking only average cooperation.

Use the distinctions in a real conversation

An adviser, platform or seller may have expertise and an incentive to steer your action. That combination invites an audit rather than automatic trust or automatic rejection. Ask for the evaluation rule, rejected alternatives and circumstances in which the recommendation would change. Those details can reveal whether a message is informative about your objective.

When the problem instead involves exchanging existing items, try top trading cycles. When a payoff table contains clearly inferior actions, try iterated dominance. A more elaborate signaling story is not always necessary. Choose the model around the actual allocation, information and commitment problem, then keep its conclusions within those assumptions.