Experiment 11 Signals and Information
Should You Believe the Signal?
Buy from a seller who knows the quality. Check whether the signal is too costly for a low-quality seller to copy.
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Start with “Work It Out, Step by Step” below. The optional expert section explains its symbols as you go. For more examples, use the plain-language math guide.
1. Make a Prediction
The Seller Knows More Than You
You are a buyer. A seller knows whether its product has high or low quality; you see only whether it used a signal. This difference in what people know is called asymmetric information. A signal is an observable action that might reveal hidden information, such as paying for a product demonstration or providing a costly warranty.
2. Make Your Choice
3. Reveal the Incentives
Would a Different Seller Copy It?
The simulated sellers follow a proposed pattern. That lets you check the quality percentage implied by the pattern. Then inspect whether each kind of seller would earn more by breaking it. A pattern that sellers want to break is not a dependable prediction, even if its quality percentage looks convincing.
Separating means different types choose different actions, so the action distinguishes them. Pooling means both types choose the same action, so the action alone does not distinguish them. A seller’s type here means its hidden quality, not a personality. A profitable deviation means changing one’s own action and earning more while others keep their rules.
4. Change One Assumption
Make the Signal Easier to Copy
Try a cheap claim, a statement that costs either type nothing: set both costs to 0. Then try a warranty that is expected to cost a reliable seller 2 points and an unreliable seller 20. A warranty is a promise to repair or repay if something fails. This model compresses its expected repair cost into one number; it does not simulate individual failures or repayments.
High quality is worth 20 points to the buyer; low quality is worth 6. The plain price is 10. A signal adds the chosen extra price. Its cost is paid before the sale and is lost even when the buyer declines. The incentive check assumes buyers purchase when their average expected value covers the price, including a tie. You may choose differently in the interactive round.
The prior is the quality percentage before seeing the action; the posterior is the revised percentage after seeing it. Both depend on the proposed pattern. If an action never occurs in that pattern, the model assumes a buyer falls back to the prior after seeing it. This is an explicit belief choice, not something the data prove. The seed reproduces the same sequence of seller types. Production costs, repair outcomes, and future reputation are omitted.
Work It Out, Step by Step
Imagine 100 sellers: 50 high quality and 50 low quality.
- If all 100 signal, 50 of the 100 signals come from high-quality sellers. Seeing the signal still gives a 50% high-quality share.
- If only the 50 high-quality sellers signal, all 50 signals come from high-quality sellers. That gives a 100% share, if sellers actually follow that pattern.
- Check the starting costs. A high-quality seller earns \(18-2=16\) points by signaling and selling. A low-quality seller copying the signal would earn \(18-20=-2\).
- In that pattern, a plain product is known to have low quality, worth only 6. At a price of 10 the modeled buyer declines, so a plain seller earns 0.
- The high-quality seller prefers 16 to 0; the low-quality seller prefers 0 to a loss of 2. Now reduce the low-quality signal cost to 0. Copying would earn it 18, so the proposed pattern no longer holds up.
In words: receiving 18 and paying 20 loses 2 points, which is less than the zero earned by not selling. The symbol \(<\) means “less than.” A costly signal helps only when the incentives make imitation unattractive.
For experts: formal model and assumptions
How to Read the Symbols
- \(H\), \(L\), and \(S\)
- \(H\) means high quality, \(L\) means low quality, and \(S\) means observing a signal. These letters label events, things that could happen.
- \(p\), \(q_H\), and \(q_L\)
- \(p\) is the high-quality fraction before seeing a signal. \(q_H\) is the fraction of high-quality sellers who signal; \(q_L\) is the fraction of low-quality sellers who signal. Fractions here run from 0 to 1. The small H and L are labels. In this app’s three patterns, each \(q\) is either 0 or 1.
- \(P(H\mid S)\)
- Read “probability of high quality, given a signal.” Probability is a chance written from 0 to 1; the vertical bar means “given that we observed.” It does not mean division.
In words: count the high-quality sellers who signal, then divide by all sellers who signal. This update is called Bayes’ rule. The top of the fraction is the numerator; the bottom is the denominator. When the denominator is zero, the pattern predicts no signal, so that calculation cannot be made. The app’s prior fallback supplies an explicitly assumed belief for that case.
Write the posterior as a fraction \(z\) from 0 to 1; for example, 50% becomes \(z=0.5\). The buyer’s average value is \(20z+6(1-z)\): value of high quality times its chance, plus value of low quality times its chance. The buyer rule purchases when this is at least the asking price. Seller profit equals any sale payment minus signal cost. The incentive check compares both possible actions for both types. It tests the selected pure pattern, meaning each type chooses one action with certainty, under the displayed off-pattern beliefs. It does not enumerate all possible signaling equilibria, stable combinations of strategies and beliefs.
The conditional probability guide explains priors, posteriors, and the “given” bar with everyday examples.
5. Transfer the Lesson
Would the Claim Be Easy to Imitate?
Two software vendors promise reliable service. One offers an enforceable refund when service fails. What would make that promise more costly for an unreliable vendor? What would you need to know about enforcement, pricing, and past failures before trusting the signal?
Concept reference: MIT’s notes on signaling, pooling, and separation. The prices, product values, and proposed patterns here are a small teaching model.
A Model Is a Place to Start
These small models make the incentives visible. Their results follow from their stated rules; they are not forecasts of how every person or organization behaves. A simulated strategy is a rule, not a personality.
Scenario links save the controls and random seed. To reproduce an interactive run, make the same choices in the same order. Changing a setting restarts the experiment.