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Screening and Contract Design

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Adverse SelectionIncentive Compatibility→
contract-theory screening self-selection

Core Idea

In screening, the uninformed principal moves first by offering a menu of contracts. Informed agents self-select into contracts based on their type. The principal designs contracts so that incentive compatibility is satisfied: each type prefers the contract meant for them. Example: insurance companies offer plans with different deductibles to reveal risk types.

Explainer

From adverse selection, you know that when one party has private information about their type, market outcomes can be severely distorted — the lemons problem shows how markets can unravel entirely. From incentive compatibility, you know that mechanism design must respect agents' ability to misrepresent themselves. Screening is the uninformed party's strategic response to this problem: instead of trying to observe the hidden information directly, the principal designs a menu of options that induces agents to *reveal* their types through their own choices.

The classic example is an insurance company that cannot directly observe whether a customer is high-risk or low-risk. If it offers a single policy, adverse selection kicks in — high-risk customers are more eager to buy, premiums rise, and low-risk customers may exit. Instead, the company offers a menu of contracts: one with a low deductible and high premium, another with a high deductible and low premium. The key design principle is that high-risk customers, who expect to file many claims, will prefer the low-deductible plan (paying more upfront but less per claim). Low-risk customers, who rarely file claims, will prefer the high-deductible plan (paying less upfront and absorbing the rare loss). The customers' own choices separate them by type — the contract menu acts as a self-selection device.

For this to work, the menu must satisfy two constraints. The incentive compatibility constraint (IC) requires that each type genuinely prefers the contract designed for them over any other option on the menu. If the low-deductible plan were too cheap, low-risk types would take it too, defeating the purpose. The individual rationality constraint (IR, also called the participation constraint) requires that each type prefers their designated contract to no contract at all — otherwise they simply walk away. The principal's optimization problem is to maximize profit (or minimize cost) subject to these IC and IR constraints.

A critical result in screening theory is that the principal can typically extract the full surplus from the lowest type (making their IR constraint bind — they are just barely willing to participate) while leaving information rents to higher types. In the insurance example, low-risk customers get a plan that is just barely acceptable, while high-risk customers get a more generous plan — not out of kindness, but because that generosity is what prevents low-risk types from mimicking high-risk types. The information rent is the cost the principal pays for being uninformed: it is the premium that must be offered to prevent profitable misrepresentation.

Compared to the full-information benchmark, screening always involves a distortion of the contract offered to at least one type. The principal typically distorts the low type's contract downward (less coverage, less quantity, lower quality) to make it unattractive to the high type, thereby preserving separation. The high type's contract is often efficient (no distortion) — a result known as "no distortion at the top." This pattern appears across screening applications: quantity discounts that offer less-than-efficient small packages, airlines that make economy class deliberately uncomfortable, software companies that cripple basic versions. In each case, the distortion is not arbitrary — it is the precise cost of eliciting truthful self-selection in a world where the principal cannot observe what the agent knows.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Literal Equations → Slope-Intercept Form → Point-Slope Form → Writing Linear Equations → Parallel and Perpendicular Line Slopes → Graphing Linear Equations → Piecewise Functions → One-Sided Limits → Continuity Definition → Limits and Continuity in Multiple Variables → Functions of Several Variables → Continuity in Multiple Variables → Partial Derivatives: Definition and Computation → Differentiability in Multiple Variables → Differentiability in Multivariable Functions → Total Differential and Linear Approximation → Chain Rule for Multivariable Functions → Implicit Differentiation → Related Rates → Optimization Problems → Critical Points of Multivariable Functions → Critical Points and Classification of Extrema → Second Partial Test for Local Extrema (Hessian) → The Hessian Matrix and Second Derivative Test → Unconstrained Optimization: Finding Extrema → Optimization in Multiple Variables → Lagrange Multipliers → Constrained Optimization and Lagrange Multipliers → Utility and Preferences → Marginal Utility and Diminishing Returns → Profit Maximization → Perfect Competition → Shutdown and Breakeven Decisions → Monopoly → Monopolistic Competition → Oligopoly and Strategic Behavior → Game Theory Basics → Nash Equilibrium → Nash Equilibrium Refinements → Strategic Form Games and Nash Equilibrium → Extensive Form Games and Game Trees → Subgame Perfect Equilibrium → Perfect Bayesian Equilibrium → Pooling and Separating Equilibria → Adverse Selection and Screening Mechanisms → Insurance Markets with Adverse Selection → Adverse Selection → Screening and Contract Design

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