Cheap talk is communication whose message has no direct effect on payoffs and does not bind future actions. It can still affect beliefs and therefore decisions. A credible commitment is an arrangement that makes a future course of action believable by restricting choices or changing the payoff from departing from it. For a quant interpreting a counterparty’s announcement, the distinction is whether the statement merely describes an intention or comes with incentives that support it.
“Cheap” describes the message’s role in the model, rather than its tone or length. A polished forecast and a casual remark can face the same strategic problem: would the speaker want you to act differently if the private information were different? The sender–receiver framework in Crawford and Sobel’s original paper, §§1–2, makes that incentive question explicit.
“High value” is not evidence by itself
Consider a fictional, one-shot asset recommendation. A sender privately observes the asset’s terminal value, 0 or 4 payoff units, with equal prior probabilities. A receiver may buy one unit at price 3, or skip. Both maximise expected payoffs; there is no discounting or risk aversion. Buying gives the receiver ; skipping gives zero.
The sender earns 1 unit whenever the receiver buys, regardless of the value, and zero otherwise. Treat that as a separate sponsor-funded fee, already outside the receiver’s stated purchase cost. The sender does not own the asset. It can send either “High” or “Low”; neither message costs anything, creates a liability or can be verified within this game. Everyone knows these rules and the prior. This is a small Bayesian game: the sender’s private value is its type.
Suppose the receiver plans to buy after High and skip after Low. A high-value sender likes that policy. But a low-value sender also wants to say High: it earns 1 instead of zero. Truthful disclosure fails the sender’s incentive test, even though the receiver would benefit from knowing the value.
One equilibrium instead has both types say High and the receiver ignore either message. After the pooled High message, the receiver’s posterior probability of value 4 remains one-half. Its expected value and expected buying payoff are
It skips because . Specify the same prior belief and Skip response after the unused Low message. Neither sender can gain by switching messages, because either message induces Skip. The receiver is best-responding to its beliefs. This is a babbling equilibrium: the message conveys no information about the type. The word High has no power to make the receiver assign a high value.
That result is specific to the stipulated incentives. It is not a theorem that cheap talk is always useless. Crawford and Sobel show how partial information transmission can survive preference differences in their model. Costlessness alone does not settle credibility; the interaction of preferences, messages and responses does. Strategic Information Transmission, §§1–2.
Change the incentives, then test the statement again
Now change the game. Before learning the value, the sender enters an observable, funded arrangement that automatically deducts 2 units if it says High when the value is 0. Assume a trusted mechanism verifies the value after the message, enforcement is certain, and the sender cannot withdraw the funds or cancel the obligation. The penalty is incurred for the false message whether or not a purchase follows. Ignore funding costs.
Those are additional capabilities, especially later verification; they were absent from the cheap-talk game. A promise to pay a penalty without a collection mechanism would leave the key problem unresolved. Polak’s Yale lecture, chapters 3–4, explains how changed incentives and collateral can alter later choices.
Test the same receiver rule: Buy after High, Skip after Low.
| Sender’s private value | Payoff from High | Payoff from Low | Preferred message |
|---|---|---|---|
| 0 | Low | ||
| 4 | High |
Now both types prefer truthful messages. With those strategies, the receiver knows High means value 4 and buys for a payoff of ; Low means value 0, so it skips rather than lose 3. Truthful communication is an equilibrium of the changed game. This establishes a supporting equilibrium, not uniqueness or a prediction that players automatically coordinate on it.
Original fictional game. The left panel is an equilibrium without enforcement. The right tests a truthful-response policy in two games: only the enforceable penalty makes the low-value sender prefer truthful disclosure.
The commitment is to the enforceable payoff rule. Its benefit comes from changing the low-value sender’s incentive to imitate. If collection occurs only with probability , a two-unit penalty gives that sender an expected payoff of from inducing a purchase. Strict preference for truthful Low requires ; at the sender is merely indifferent. A large nominal penalty can accomplish little if enforcement is unlikely.
What is actually constrained?
Use backward induction to ask what the speaker would prefer when a promised future action becomes due. Commitment needs a specified mechanism and must be known to the party whose response it is meant to change. It can sacrifice useful flexibility; it need not improve joint welfare. These are central cautions in Polak’s discussion of commitment, chapter 4.
Commitment and costly signalling can overlap, but they answer different questions. Signalling asks what an observed action reveals about a private type. Commitment asks what future actions or payoffs have changed. Spending money on an announcement does not by itself make a later promise enforceable.
For a trading application, write down the private information, the sender’s economic objective and what happens after a statement proves false. Repeated interaction and reputation may supply incentives, but they require their own continuation payoffs. Neither the babbling outcome nor the penalty arrangement above is a calibrated model of actual counterparties.
Sources
- Vincent P. Crawford and Joel Sobel, Strategic Information Transmission, Econometrica 50(6), 1982, pp. 1431–1451; §§1–2, pp. 1431–1434: sender–receiver incentives, equilibrium beliefs, communication without direct signalling costs and the possibility of partial information transmission. The binary asset and penalty examples here are original teaching games, not the paper’s continuous-type model.
- Ben Polak, Sequential Games: Moral Hazard, Incentives, and Hungry Lions, Yale ECON 159, 2007; chapters 3–4: incentive design, collateral, changed future payoffs and why the other player must know about a commitment. The lecture is used for game-theory reasoning, not current legal rules about collateral or enforcement.