💻 computer science

The Inference Bottleneck: A Formal Model of Vertical Foreclosure in AI Markets

This paper presents a formal game-theoretic model demonstrating how AI providers can vertically foreclose downstream rivals through non-price mechanisms like quality-of-service discrimination and routing bias, offering a calibrated risk assessment of major providers and proposing a "Neutral Inference" regulatory framework to mitigate these anti-competitive effects.

Original authors: Gaston Besanson

Published 2026-04-21

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Gaston Besanson

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of Artificial Intelligence as a massive, bustling city. In this city, there are a few giant companies (like Google, OpenAI, Microsoft, and Anthropic) that own the power plants. These power plants generate the electricity needed to run everything: the lights, the factories, the traffic lights, and the homes.

In the AI world, this "electricity" is called Inference. It's the computing power that makes an AI actually think and answer a question.

This paper, written by Gaston Besanson, is a warning label and a rulebook for what happens when the owner of the power plant also owns the most popular factory in the city.

The Core Problem: The "Selfish Landlord"

The paper asks a simple question: What happens when the landlord of the apartment building also runs the best coffee shop in the lobby?

If the landlord wants to make their coffee shop the most popular, they might be tempted to:

Turn down the heat for the other coffee shops in the building (making their coffee cold and slow).
Hide the signs pointing to the other shops, so everyone walks straight to the landlord's shop.
Keep the "VIP Espresso Machine" locked in a back room, only letting their own shop use it, while the others have to use a broken, old machine.

The paper calls this "Vertical Foreclosure." It's not about the landlord lowering prices to kill the competition (predatory pricing); it's about sneaky discrimination. They don't have to be cheaper; they just have to make the competition's product feel "stuck," "slow," or "dumber."

The Three Ways They Do It

The paper identifies three specific tricks the "Landlord" uses:

1. The "Slow Lane" (Quality of Service Discrimination)
Imagine you order a pizza. If you order from the landlord's own app, the driver arrives in 10 minutes. If you order from a rival pizza place, the driver takes 45 minutes, gets lost, or forgets the cheese.

In AI terms: The big company makes their own AI chatbot fast and smart, but makes the API (the connection) for rival developers slow, buggy, or limited. This makes the rival's app feel terrible, so users switch to the landlord's app.

2. The "Fake Map" (Routing Bias)
Imagine the landlord controls the city's GPS. When you ask, "Where is the best coffee?", the GPS thinks it's being helpful, but it secretly reroutes everyone to the landlord's shop, even if a rival shop is right next door and has better reviews.

In AI terms: When you ask a smart assistant (like a digital secretary) to find a tool to write code, the assistant secretly picks the landlord's tool, even if a rival's tool is objectively better.

3. The "VIP Only" Room (Tier-Based Access)
This is the newest trick. Imagine the landlord builds a super-fancy espresso machine that makes the best coffee in the world. They put it in a room called "Project Glasswing." They tell their own coffee shop, "You can use this." But they tell all the other coffee shops, "Sorry, this machine is too dangerous/complex for you. You can only use the old one."

In AI terms: The company releases a super-smart AI model to their own products but keeps it hidden from competitors, claiming it's for "safety" or "testing," when really it's just to keep the competition in the dark.

The "Math" of the Problem

The paper uses a lot of math (game theory) to prove that this isn't just a bad habit; it's a profitable strategy.

The Trade-off: The landlord has to choose between making money by selling electricity to everyone (API fees) or making money by crushing the competition in the coffee shop (selling more coffee).
The Tipping Point: The math shows that if the coffee shop is very profitable, and the electricity is essential for the coffee to work, the landlord will always choose to sabotage the other shops. It doesn't matter how "important" the electricity is; if the landlord's own shop makes enough money, they will degrade the service for everyone else.

The "Risk Map" (Who is doing it?)

The authors applied their model to the real world (as of April 2026) to see who is most likely to be the "Selfish Landlord":

Google & OpenAI: High Risk. They own the power plant and have massive, popular consumer apps (Search, ChatGPT). The math says they have the strongest incentive to slow down their rivals.
Microsoft: Mixed Bag. They own the power plant (via Azure) and have a huge office suite (Copilot). However, the paper notes they are currently "voluntarily" playing fair by letting rival models (like Anthropic's) run on their system. The paper suggests this is because they are scared of regulators and competition.
Anthropic: Split Personality.
- Consumer side: Low risk. They rely on selling electricity to others, so they don't want to hurt their customers.
- Enterprise side: High risk. In the world of "coding agents" (AI that writes code), Anthropic has its own product (Claude Code) competing with rivals using the same API. Here, the temptation to sabotage rivals is high.

The Solution: "Neutral Inference"

The paper doesn't suggest breaking up the companies (which would be like forcing the landlord to sell the power plant). Instead, it proposes a Conduct Framework called Neutral Inference. Think of it as a "Fair Play" rulebook for the landlord:

QoS Parity: If you sell electricity to a rival, it must be the same speed and quality as what you use for yourself. No "slow lanes."
Routing Transparency: If your GPS reroutes people, you have to show the map. You can't secretly hide the best shops.
Fair Pricing: You can't charge rivals more just to hurt them.
Tier Transparency: If you have a "VIP Room" with a super-machine, you have to explain why it's locked. If it's for safety, prove it. If it's just to keep rivals out, you have to open the door.

The Bottom Line

The paper argues that if we don't stop this behavior, the AI market will tip. The big companies will become so dominant that no new, creative AI apps can survive. The result? We all get stuck with the same few products, innovation stops, and the "electricity" becomes more expensive and worse for everyone.

The solution isn't to break the giants apart, but to force them to be neutral landlords: treat their own tenants and the rival tenants exactly the same. If they do, the paper estimates we could save the economy tens of billions of dollars a year in lost innovation and wasted time.

1. Problem Statement

The paper addresses a fundamental shift in competitive dynamics within the generative AI market: the transition from competition based on one-time model training to competition based on continuous inference, distribution, and routing.

As vertically integrated firms (e.g., Google, OpenAI, Microsoft, Anthropic) control "cognitive infrastructure" (scalable inference APIs) while simultaneously competing downstream with their own applications, they face incentives to engage in non-price vertical foreclosure. Unlike traditional antitrust concerns focused on predatory pricing, this paper investigates how upstream providers can profitably degrade the quality of service (QoS) for downstream rivals or bias routing decisions without lowering prices, thereby "raising rivals' costs" and foreclosing competition.

The paper specifically aims to:

Formalize the economic incentives for non-price discrimination in AI inference markets.
Model a new mechanism: tier-based access discrimination (gating access to frontier model classes).
Bridge the gap between abstract economic theory and regulatory observables to create a usable framework for antitrust enforcement.

2. Methodology

The paper employs a formal game-theoretic model combined with a stylized calibration based on public data as of April 2026.

A. Theoretical Framework

Market Structure: A two-layer market with one upstream provider ( $U$ ) controlling inference infrastructure and $N$ downstream rivals ( $i$ ). $U$ also operates a downstream application.
Demand: Consumers choose among applications using a Logit demand model, where utility depends on application quality ( $Q$ ) and price ( $p$ ).
Quality Aggregation: Final application quality is a function of inference quality ( $q$ ) and application-layer effort ( $e$ ): $Q_i = \alpha q_i + (1-\alpha)e_i$ . Here, $\alpha$ represents the importance of inference quality.
Cost Structure: Upstream infrastructure costs are quadratic in quality ( $q^2$ ), with a term ( $\phi$ ) capturing economies of scope when serving both first-party and third-party workloads.
Timing:
1. Stage 1: $U$ commits to API terms (price $p$ , own quality $q_U$ , rival quality $q_i$ ). Rivals decide on entry based on these terms.
2. Stage 2: Active firms choose effort levels and set prices; consumers choose.

B. Extensions

The baseline model is extended to include:

Dynamic Foreclosure: A two-period model where providers offer generous access initially to lock in ecosystem development, then degrade QoS once switching costs are high.
Routing Bias: Modeling how an upstream provider operating a user-facing assistant can bias traffic toward its own tools.
Tier-Based Access: A mechanism distinguishing between a "baseline" model (generally available) and a "frontier" model (restricted access), parameterized by a tier gap ( $\tau$ ) and partner exclusivity ( $\kappa$ ).

C. Calibration & Identification

The paper explicitly distinguishes between structural estimation (which it does not perform) and comparative risk mapping.

Parameters: Distinguished as Observable (e.g., market share), Inferred (e.g., integration breadth $\lambda$ ), or Judgment-based (e.g., switching costs $S$ ).
Sensitivity Analysis: Results are tested against perturbations in key parameters to ensure robustness.
Data Source: Uses public adoption data from April 2026 for Google, OpenAI, Microsoft, and Anthropic.

3. Key Contributions

The paper makes four distinct theoretical and practical contributions:

Formal Model of Non-Price Foreclosure: It derives the conditions under which a vertically integrated provider profitably degrades third-party QoS. It proves that discrimination is driven by a trade-off between downstream business-stealing gains and API revenue losses.
Tier-Based Access Discrimination: It identifies a distinct foreclosure mechanism where providers gate access to superior model classes (frontier tiers). Unlike standard QoS discrimination, this generates durable rents not subject to competitive erosion in the baseline market.
Transparent Calibration Methodology: It provides a replicable framework for "comparative risk mapping," explicitly stating the provenance of parameters and treating firm-level outputs as risk indicators rather than structural estimates.
Model-to-Observables Bridge: It maps latent model primitives (e.g., $\alpha, \lambda, \tau$ ) to specific regulatory observables (e.g., latency differentials, partner set composition), enabling practical enforcement.

4. Key Results

A. Equilibrium Characterization (Proposition 1)

The paper derives an explicit local equilibrium characterization of the QoS gap ( $\Delta q^* = q^*_U - q^*_i$ ):
$\Delta q^* = \frac{1}{\gamma} \left( \alpha \cdot m_U \cdot s_U [(1-s_U) + s] - \frac{p \rho \eta}{q^*_i} \right)$

Discrimination Condition: Discrimination occurs ( $\Delta q^* > 0$ ) if and only if the marginal gain from stealing downstream market share exceeds the marginal loss in API revenue.
Comparative Statics: The gap is:
- Increasing in the importance of inference quality ( $\alpha$ ) and downstream margins ( $m_U$ ).
- Decreasing in API access prices ( $p$ ) and rival entry elasticity ( $\eta$ ).
Refinement: Discrimination is not determined by a simple threshold on $\alpha$ alone, but by a joint boundary in the space of margins, prices, and elasticities.

B. Welfare Effects (Proposition 2)

Foreclosure creates a welfare loss composed of:

Direct Quality Loss: Rivals provide lower quality than the social optimum.
Effort Multiplier: Degraded QoS reduces rivals' incentive to invest in application-layer effort.
Business-Stealing Deadweight Loss: Demand shifts to the integrated firm not due to superior intrinsic quality, but due to artificial degradation of rivals.

C. Tier-Based Access (Proposition 5)

The model shows that foreclosure gains increase monotonically with the tier gap ( $\tau$ ) and partner exclusivity ( $\kappa$ ). This mechanism creates "capability rents" that persist as long as the frontier model is withheld, distinct from standard QoS competition.

D. Comparative Risk Mapping (April 2026 Data)

Applying the model to four major providers yields the following risk assessments:

Google (Gemini): Highest Risk. High integration ( $\lambda \approx 0.92$ ), high downstream margins, and significant market share create strong incentives for a large QoS gap (implied $\approx 0.27$ ).
OpenAI (GPT): Elevated Risk. High consumer reach and subscription margins imply a significant QoS gap (implied $\approx 0.20$ ), overlapping with Google's risk profile.
Microsoft (Copilot): High Structural Capacity, Constrained Realized Conduct. While structurally capable of foreclosure (high $\lambda$ ), observed routing bias is voluntarily constrained (likely due to competition and regulatory scrutiny), resulting in a lower realized risk.
Anthropic (Claude): Split Position.
- Consumer Channel: Low Risk. The dominance of enterprise API revenue makes degrading the API unprofitable.
- Enterprise Coding-Agent: Elevated Risk. Vertical integration in this submarket (Claude Code vs. API rivals) creates incentives for discrimination.
- Cybersecurity Tier (Project Glasswing): Tier-Gated. High $\tau$ and $\kappa$ trigger tier-gating criteria, though current conditions suggest a potential "safety carve-out" if transparency obligations are met.

5. Significance and Policy Implications

A. Regulatory Framework: "Neutral Inference"

The paper proposes a four-pillar conduct framework to mitigate these risks:

QoS Parity: Mandate non-discriminatory latency, throughput, and feature access for rivals.
Routing Transparency: Require auditable records of how user requests are routed to tools.
FRAND-style Non-Discrimination: Prevent discriminatory pricing or terms that handicap rivals.
Tier Transparency & Release Pathway: For restricted-access tiers, require purpose justification, audit of partner sets, and a clear technical pathway to general availability.

B. Welfare Impact

Illustrative calculations suggest that non-intervention could result in annual welfare losses in the range of $35B to $95B. Implementing the "Neutral Inference" framework could generate net welfare gains of $40B–$ 55B annually, even after accounting for potential innovation offsets.

C. Contribution to Antitrust Theory

This paper refines the understanding of vertical foreclosure in digital markets by:

Moving beyond price-based theories to quality-based discrimination.
Introducing tiered access as a distinct foreclosure mechanism relevant to frontier AI.
Providing a practical enforcement toolkit that translates complex economic models into measurable regulatory triggers, moving antitrust analysis from theoretical abstraction to operational reality.

In conclusion, the paper argues that in the AI era, control over inference infrastructure constitutes a bottleneck that requires conduct-based regulation to prevent the "picking of winners" by vertically integrated incumbents, while preserving incentives for innovation through carefully calibrated tolerance thresholds.