Better Models Can Reduce Accuracy Under Strategic Pricing

Recent progress in language models is assessed against fixed computation budgets, but provider prices may change when they compete for users. We show that a model can become more accurate at every computation level and can generate higher equilibrium revenue, yet users on a fixed budget may incur lower accuracy after providers change prices. We model the market of combining verifiable outputs from models priced independently by providers, and show that every pure-strategy equilibrium is characterized by the maximizers of $x{f}^{\prime }(x)$, where $f$ is the negative log failure probability. This characterization allows us to identify an explicit family of improvements that reduces equilibrium accuracy on an open parameter region, even when each task is eventually solvable, and holds under sufficiently small strictly positive serving costs. We perform experiments with 610,560 Qwen and Llama generations on LiveCodeBench and MATH-500, comparing fixed vs. equilibrium prices. Non-thinking replacements have gains of 3.8 and 2.2 percentage points from checkpoints at fixed prices, but become losses of 1.7 and 1.6 points after repricing. Thinking replacements have gains that remain positive, but are reduced by 1.4 and 0.5 points respectively. Moreover, we bound profitable price deviations discuss the implications of these results for the shape of test-time scaling curves.