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arXiv · 2604.17431

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

Gaston Besanson
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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.

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Gaston Besanson. 2026-04-19. The Inference Bottleneck: A Formal Model of Vertical Foreclosure in AI Markets. https://arxiv.org/abs/2604.17431

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