Information Intermediaries in Monopolistic Screening

This paper demonstrates that in a monopolistic screening environment, an information intermediary biased toward high-quality products but prioritizing consumer surplus induces the monopolist to expand its product range, a strategic shift that paradoxically reduces overall economic efficiency compared to direct information provision.

The Gist

The Big Picture: The Mystery Box and the Guide

Imagine you are walking into a store to buy a laptop. You don't actually know what you need. You don't know if you are a "casual browser" who just needs to check email, or a "power user" who needs to edit 4K video. You are holding a Mystery Box of your own needs, but you can't see inside it.

In this story, there are three main characters:

1. The Seller (The Monopolist): A shop owner who makes laptops of different qualities (Basic, Pro, Ultra). They want to make the most money.
2. The Consumer (You): The buyer who wants a good deal but doesn't know their own needs yet.
3. The Intermediary (The Guide): A tech reviewer, an influencer, or a smart app that looks inside your Mystery Box and tells you, "Hey, you're actually a power user!"

The Twist: The Guide isn't 100% neutral. They love high-end, fancy products. They want you to buy the "Ultra" laptop because it makes them look like an expert, even if a "Basic" laptop would save you money.

The Game: Who Moves First?

In the real world, the shop owner usually sets up the shelves before the Guide gives advice.

1. Step 1: The Seller puts a menu of laptops on the shelf (e.g., "We have Basic, Pro, and Ultra").
2. Step 2: The Guide looks at the menu, looks at you, and says, "Based on what's on the shelf, here is what you should buy."
3. Step 3: You buy the laptop.

The Seller knows the Guide is biased. So, the Seller has to design the menu not just to trick you, but to trick the Guide into giving advice that helps the Seller make money.

The Main Discovery: The "More Options" Paradox

The paper finds a surprising result about what happens when the Guide becomes less biased (i.e., when the Guide starts caring more about your wallet and less about selling the fanciest laptop).

Intuition says: If the Guide is fairer and helps you find the perfect laptop for your needs, the market should get more efficient. Everyone wins.

The Paper says: Actually, it gets messier.

Here is the analogy:
Imagine the Seller is a chef.

• Scenario A (Biased Guide): The Guide only recommends the "Super Deluxe Steak." The Chef knows this, so they only cook one thing: The Super Deluxe Steak. They make a huge profit.
• Scenario B (Fair Guide): The Guide starts telling people, "Actually, you might just want a burger." The Chef realizes, "Oh no, if I only have the Steak, I'll lose all the burger lovers."
• The Reaction: To stop losing customers, the Chef decides to cook 20 different types of burgers, 15 types of sandwiches, and 30 types of salads.

The Result:

• You (The Consumer): You are happier! You finally found the perfect burger. You have more choices.
• The Chef (The Seller): They are making less money. Why? Because cooking 50 different dishes is expensive and chaotic. They can't charge as much for a burger because you know exactly what you want.
• The Economy: Surprisingly, the total "happiness" (efficiency) of the whole system goes down. The cost of managing 50 different dishes outweighs the benefit of you finding the perfect burger.

Why Does This Happen?

The paper explains that when the Guide is very biased (loves high quality), the Seller can get away with offering just one high-quality product. The Guide pushes everyone to buy it, and the Seller makes a killing.

But when the Guide becomes fairer, the Seller is forced to offer more variety to keep everyone happy.

• The Seller tries to "screen" you (figure out if you are a burger lover or a steak lover) by offering many options.
• This creates a lot of "noise" and complexity.
• The cost of producing all these different options eats up the profits.
• Even though you get a better deal, the system as a whole becomes less efficient because the Seller is wasting resources trying to cater to every tiny preference the Guide reveals.

The "Goldilocks" Zone for Consumers

The paper also finds something weird about what consumers prefer.

• You might think you want a Guide who is 100% neutral (0% bias).
• But the paper shows that sometimes, a Guide who is slightly biased toward high quality is actually better for you than a Guide who is extremely biased.
• Why? If the Guide is too neutral, the Seller panics and offers too many confusing options, raising prices or lowering quality to cover costs. If the Guide is slightly biased, the Seller offers a "sweet spot" of options that keeps prices reasonable while still giving you good variety.

Real-World Takeaway

This explains why we see so many different models of iPhones, cars, or streaming plans.

• When tech reviewers are very "hype-driven" (biased toward the newest, most expensive tech), companies might just push one flagship product.
• When reviewers become more balanced and tell us, "Hey, the mid-range phone is actually great," companies are forced to flood the market with mid-range, budget, and pro options to capture every type of buyer.

The Lesson for Policymakers:
Just because we want "more information" and "fairer guides," it doesn't always mean the market will work better. Sometimes, having a perfectly fair guide forces companies to create a chaotic, expensive, and inefficient marketplace. The best policy isn't always "maximum transparency"; it's finding the right balance where the Seller can still offer a good variety without going bankrupt trying to please everyone.

Summary in One Sentence

When a helpful guide starts telling consumers exactly what they need, the seller is forced to offer a dizzying array of choices to keep up, which makes the consumer happier but the seller poorer and the whole economy slightly less efficient.

Technical Summary

1. Problem Statement

The paper investigates a monopolistic screening environment where a seller offers a menu of quality-differentiated products to a consumer. The core novelty lies in the information structure:

• Unknown Valuation: Unlike standard screening models (e.g., Mussa and Rosen, 1978) where the consumer has private information about their valuation ($\theta$), here neither the seller nor the consumer knows $\theta$ initially.
• The Intermediary: A third-party intermediary (e.g., a review platform, influencer, or advisor) possesses the ability to reveal information about $\theta$ to the consumer.
• Intermediary's Objective: The intermediary aims to maximize consumer surplus but is biased toward higher-quality products. Their utility is defined as $U_I = (\theta + b)q - t$, where $b \geq 0$ represents the bias toward quality.
• Strategic Interaction: The game proceeds in three stages:
  1. The monopolist posts a menu of contracts $(q, t)$.
  2. The intermediary commits to an information structure (signal) to reveal to the consumer.
  3. The consumer observes the signal and chooses a menu item.

The central research question is: How does the monopolist optimally design a finite-item menu in response to the intermediary's bias, and how does this affect market efficiency, profits, and consumer welfare?

2. Methodology

The authors employ a combination of Mechanism Design and Bayesian Persuasion (Kamenica and Gentzkow, 2011).

• Model Setup:
  • Consumer utility: $U_B = \theta q - t$.
  • Intermediary utility: $U_I = (\theta + b)q - t$.
  • Seller cost: $c(q)$, strictly increasing and convex.
  • Prior distribution: $\theta \sim F_0$ on $[0, 1]$, assumed to be Myerson regular (increasing hazard rate).
• The Constraint (Obedience): Since the intermediary moves after the menu is posted, the seller must ensure the intermediary has no incentive to deviate from the information structure that benefits the seller. This creates an obedience constraint (I-OB). The seller effectively chooses the menu and the resulting distribution of posterior means ($G$) that the intermediary will find optimal to induce.
• Mathematical Tools:
  • Dual Price Functions: The authors utilize the framework of Dworczak and Martini (2019) and Arieli et al. (2023) to solve the intermediary's persuasion problem. They characterize the optimal information structure as a bi-pooling distribution (types are either fully disclosed or pooled into atoms).
  • Finite-Item Restriction: The analysis focuses on finite-item menus, justified by real-world fixed costs of variety and theoretical tractability.
  • Uniform-Quadratic Benchmark: To derive comparative statics, the authors specialize the model to a uniform prior and quadratic cost function ($c(q) = q^2/2$).

3. Key Contributions

1. Characterization of Optimal Menus under Intermediary Bias: The paper provides a complete characterization of the profit-maximizing finite-item menu as a function of the intermediary's bias $b$.
2. Endogenous Product Variety: It demonstrates that the number of products offered is endogenous to the intermediary's bias. As the intermediary becomes less biased (more aligned with consumer surplus), the monopolist is forced to expand the product range (increase the number of items) to maintain profitability.
3. Non-Monotonic Welfare Effects: The paper reveals that consumer surplus and economic efficiency do not change monotonically with the intermediary's bias. There are regimes where a highly biased intermediary might actually yield higher consumer surplus than a moderately biased one, depending on the seller's strategic response.
4. Efficiency vs. Direct Disclosure: The presence of an intermediary generally leads to lower economic efficiency compared to a scenario where the seller provides information directly, due to the convexity of production costs and the strategic expansion of the menu.

4. Main Results

A. The High-Bias Regime ($b \geq b^*$)

• If the intermediary's bias toward quality is sufficiently high, the optimal mechanism coincides with the case where the seller provides information directly (Bergemann et al., 2022).
• The optimal menu is a single-item menu.
• The intermediary's bias is so strong that they effectively act as an agent for the seller, pooling low types to maximize the probability of trade for the high-quality item. The intermediary is "redundant" in terms of altering the seller's optimal strategy.

B. The Low-Bias Regime ($b < b^*$)

• As the bias decreases, the obedience constraint binds. The intermediary starts revealing more information to the consumer to maximize their own objective (consumer surplus).
• Strategic Expansion: To counteract the loss of information rents caused by better consumer learning, the monopolist strategically expands the menu.
  • The optimal number of items $N^*$ increases as $b$ decreases.
  • In the limit as $b \to 0$ (intermediary fully aligned with consumer), the optimal menu approaches a continuum of items, replicating the classic Mussa-Rosen screening outcome where the consumer effectively has private information.
• Quality Distortions:
  • The "no distortion at the top" result of standard screening holds (the highest type gets efficient quality).
  • However, the average quality in the market is lower than in the standard private-information model but higher than in the direct-disclosure model.

C. Market Outcomes and Comparative Statics

• Seller Profits: Profits are monotonically decreasing in the intermediary's bias (i.e., profits are highest when bias is high and lowest when bias is low). The expansion of the product variety mitigates but does not reverse this profit decline due to the convexity of production costs.
• Consumer Surplus: Exhibits a non-monotonic relationship with bias.
  • Consumers generally prefer low bias (more variety, better matching).
  • However, if the bias difference is small, a slightly higher bias might be preferred because it prevents the seller from expanding the menu in a way that reduces overall surplus or increases prices in specific configurations.
• Economic Efficiency: Total surplus is lower in the presence of an intermediary compared to direct seller-to-consumer information provision. The "informational friction" introduced by the intermediary forces the seller to offer a suboptimal variety of products to satisfy the obedience constraint, leading to higher production costs and lower total welfare.

D. Exogenous Constraints

If the seller is externally constrained from offering the optimal number of items (e.g., regulatory limits or fixed costs preventing variety expansion):

• Both consumer surplus and total surplus decrease further.
• The inability to expand the menu prevents the seller from mitigating the profit loss caused by the intermediary's reduced bias, leading to a "double loss" for the market.

5. Significance and Policy Implications

• Policy Design: The paper challenges the intuition that "more information is always better." While intermediaries improve consumer learning, they induce strategic responses from sellers (menu expansion) that can reduce overall economic efficiency. Policymakers must consider how sellers adapt to information transparency.
• Empirical Estimation: Researchers ignoring the role of intermediaries may misestimate market inefficiencies.
  • Using standard screening models (Mussa-Rosen) would overestimate quality distortions.
  • Using models where sellers control information (Bergemann et al.) would underestimate distortions.
• Platform Economics: The results explain why platforms (intermediaries) with different biases (e.g., "luxury-focused" vs. "budget-focused") lead to vastly different product ecosystems. A platform focused on consumer surplus forces sellers to diversify their offerings, potentially lowering average quality but increasing consumer choice.
• Strategic Advice: Sellers may prefer intermediaries with higher bias (e.g., paying influencers to highlight premium features) to avoid the costs associated with maintaining a vast, low-margin product range.

Conclusion

Kyriazis and Lou provide a rigorous framework showing that information intermediaries are not passive observers but active shapers of market structure. Their bias dictates the monopolist's product strategy, creating a trade-off between consumer learning and production efficiency. The optimal response to a less biased intermediary is not to improve quality but to increase variety, a strategy that benefits consumers in terms of choice but often at the cost of total economic efficiency.