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

TL;DR

This paper models vertical foreclosure in AI inference markets, analyzing mechanisms like QoS discrimination, routing bias, and tier-based access, with implications for competition and policy.

Contribution

It introduces a formal game-theoretic model of inference market foreclosure mechanisms and characterizes equilibrium conditions under various parameters.

Findings

QoS discrimination increases with inference-quality importance and margins.

Routing bias is constrained by a multi-model pivot, reducing foreclosure risk.

Policy proposals aim for fairness and welfare gains in AI inference markets.

Abstract

As generative AI commercializes, competitive advantage is shifting from model training toward inference, distribution, and routing. This paper develops a formal game-theoretic model of vertical foreclosure in inference markets, as the formal-model companion to Besanson and Celani (2026). The model isolates two foreclosure mechanisms operating without predatory pricing: quality-of-service (QoS) discrimination against downstream rivals via latency, throughput, context limits, or feature access; and routing bias in assistant-layer interfaces. An extension motivated by Anthropic's April 2026 release of Claude Opus 4.7 alongside the restricted-access Claude Mythos Preview introduces a third mechanism, tier-based access discrimination, parameterized by a tier gap (tau) and partner-exclusivity (kappa). The main result gives an explicit local equilibrium characterization of the QoS gap. Under logit demand and symmetric rivals, the gap is strictly increasing in inference-quality importance (alpha) and downstream margins, and strictly decreasing in API price and rival entry elasticity. Discrimination vanishes at a joint boundary rather than at a simple threshold in alpha alone. A stylized calibration to four providers using April 2026 data treats parameter values as inputs to a comparative risk mapping, not structural estimates. The mapping suggests Google and OpenAI face conditions most conducive to foreclosure; Microsoft's realized routing bias has been voluntarily constrained by a March 2026 multi-model pivot; Anthropic shows low consumer-channel risk and elevated risk in enterprise coding-agent segments. The policy section proposes Neutral Inference, a four-pillar conduct framework: QoS parity, routing transparency, FRAND-style non-discrimination, and tier transparency with release-pathway discipline. Illustrative welfare calculations suggest net gains in the tens of billions annually.