Bayesian Persuasion¶

Model how a sender who cannot lie — committed to a public, truthful signal structure faced by a Bayes-rational receiver — still shifts the receiver's action by choosing how informative the signal is, solved geometrically as the concave closure of the sender's value over posteriors.

Version: v3 · 2026-09-28 · History
Domain-specific #: 89
Domain group: Social Sciences
Origin domain: Economics & Finance
Subdomain: Game Theory → Economics & Finance

Core Idea¶

Bayesian persuasion (Kamenica and Gentzkow, 2011) is the strategic situation in which a sender commits in advance to an information experiment — a publicly binding signal whose distribution depends on the state — and a receiver observes the signal, updates by Bayes' rule, and acts. Even unable to lie and facing a fully rational receiver, the sender can profit by choosing how informative the experiment is, often committing to less than full disclosure. Geometrically, the solution is the concavification of the sender's value function over posteriors.

How would you explain it like I'm…

The True-But-Blurry Trick

You want your friend to come play outside. Before looking at the sky, you promise a rule for what you will say, and your friend knows the rule. You never break the rule or lie, but you pick a rule that says 'come out' on sunny days and on some cloudy days too. Your friend still trusts you, and ends up coming outside more often than if you told every detail.

Choosing How Much to Tell

Bayesian Persuasion is about someone who wants to nudge another person's choice without lying. The persuader must decide ahead of time, in public, exactly how their report will depend on the real facts. The listener knows this rule, looks at the report, and changes their mind sensibly. The trick is that the persuader chooses how much detail the report gives: a vaguer report can push the listener toward the choice the persuader wants more often. It only works because the persuader is stuck with the rule they announced.

Persuasion by Signal Design

In Bayesian Persuasion, a sender commits in advance to an information experiment: a publicly known rule for what signal appears in each possible state of the world. The receiver sees the signal, updates their beliefs with Bayes' rule, and acts in their own best interest. Because the receiver knows the rule, the sender cannot fool them, and on average the receiver's updated beliefs must equal what they believed before (this is called Bayes-plausibility). Even so, the sender can gain by choosing how coarse the signal is, for example lumping some weak cases in with strong ones. This differs from cheap talk, where nothing is binding and the receiver simply discounts what the sender says. Commitment is what makes the strategy work.

Bayesian Persuasion (Kamenica and Gentzkow) models a sender who commits to a signal structure, a known and binding mapping from states to distributions over signal realizations, and a Bayesian receiver who observes the realization, forms a posterior, and chooses an action. The sender's payoff depends on that action, so the sender's design problem is to pick the experiment maximizing expected payoff. The key constraint is Bayes-plausibility: the distribution of induced posteriors must average back to the prior, because signals are generated from the true state distribution. This lets the problem be restated as choosing a distribution over posteriors with mean equal to the prior. The optimal value is then the concave closure (concavification) of the sender's value-of-posterior function evaluated at the prior, and the optimal experiment is the posterior distribution attaining that hull. The striking result is that without any lying, and against a fully rational receiver, the sender often does best with partial rather than full disclosure. Commitment is essential; without it the game collapses to cheap talk, where persuasion is limited by preference alignment. Examples include a prosecutor designing what evidence to seek, credit-rating scales, stress-test disclosure levels, and recommendation structures, each a choice of informativeness rather than content.

Cross-Domain Echoes¶

See how this entry connects to another domain.

A credible promise still has a boundary

Scope of Application¶

Bayesian persuasion lives within the information-design field it founded, restaged across committed sender-receiver games with a Bayes-rational receiver and a binding public signal.

Information design in markets — prosecutor evidence design, credit-rating granularity, exam thresholds.
Regulatory disclosure — stress tests, drug labels, calorie counts a regulator tunes for informativeness.
Advertising and recommendation systems — which reviews to surface without saying anything false.
Political communication — which polls or endorsements to commission for rational voters.

Clarity¶

The concept makes legible a lever the lying-versus-truth dichotomy hides: a sender who can say nothing false still holds latitude through the design of the experiment — how informative the public signal is. It relocates a communicator's power from message content to disclosure structure, separating forbidden deception from the informativeness choice that is the whole game. It also makes commitment a load-bearing object to check for: without a binding signal structure the situation collapses to cheap talk.

Manages Complexity¶

The sprawl is the continuum of disclosure strategies — every degree of informativeness, every way of pooling states — recurring anew in each application. The concept collapses the search to one geometric operation: because the receiver acts only on their posterior, the sender's problem becomes forming the concave closure of the value-over-posteriors function and evaluating it at the prior. The analyst then tracks only the belief-to-action map and the prior, reading off whether persuasion has bite and how coarse the optimal signal is.

Abstract Reasoning¶

The concept licenses reasoning backward from the receiver's belief-to-action map and its thresholds, then concavifying the value function to read the optimal experiment off its chord. A decisive binary — is the value function concave at the prior? — predicts both whether persuasion pays and how coarse the signal should be. Bayes-plausibility guards the design as redistribution not manufacture of belief, and commitment is a precondition to verify, separating persuasion from cheap talk.

Knowledge Transfer¶

Within economic theory and information design, Bayesian persuasion transfers as mechanism: the backward reasoning, concavification, the decisive binary, and the two preconditions carry intact across application domains of one model — market information design, regulatory disclosure, recommendation systems, political communication. Beyond committed sender-receiver games the honest account is a shared insight carried by component primes — gatekeeping, framing, information_asymmetry, and commitment — of which this is one formalisation. The concavification-under-commitment machinery stays home-bound.

Relationships to Other Abstractions¶

Current abstraction Bayesian Persuasion Domain-specific

Parents (5) — outgoing typed relations

Bayesian Persuasion includes Bayesian Updating Prime

Bayesian Persuasion contains the receiver's prior-to-posterior update on each realized signal, which is the belief-to-action link the sender designs around.
Bayesian Persuasion presupposes Credible Commitment Prime

Bayesian Persuasion presupposes a publicly believable ex-ante commitment to honor the chosen signal structure after the state is realized.
Bayesian Persuasion presupposes Information Asymmetry Prime

Persuasion presupposes that the receiver lacks payoff-relevant state information that the committed experiment can selectively reveal.
Bayesian Persuasion is a decomposition of Framing Prime

Removing the game-theoretic frame leaves truthful presentation structure altering evaluation and action even though no underlying fact is falsified.
Bayesian Persuasion is a decomposition of Gatekeeping Prime

Stripping the posterior-simplex apparatus leaves selective passage control: the sender chooses which distinctions reach the receiver and at what granularity.

Hierarchy paths (8) — routes to 7 parentless roots

Bayesian Persuasion → presupposes Credible Commitment → is a kind of Commitment → is a kind of Constraint

Neighborhood in Abstraction Space¶

Bayesian Persuasion sits in a moderately populated region (50^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Persuasion & Interpersonal Communication (17 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-25