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Pricing and Competition for Generative AI
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Theoretical game-theoretic model of sequential pricing between two firms releasing generative AI models that are priced per prompt and compared by user cost-per-satisfactory-output across multiple tasks.
Problem
How should developers of generative AI models price their technology when users choose among competing models across multiple tasks, with multi-round prompting and binary satisfaction?
Approach
Models a user's choice via price-performance ratio (price per prompt divided by success probability, under geometric prompting rounds), then formulates a first-mover vs. latecomer pricing game where the latecomer ranks tasks by competitive ratio and the first mover solves a bi-level problem; under exponential demand it derives closed-form (Lambert W) solutions.
Key results
- Latecomer firm that prices after observing competitor can always secure cost-effectiveness on at least one task.
- If task performances are sufficiently similar (kappa_2/kappa_1 > a_1/(a_1+a_2)), the first-to-market firm may be cost-ineffective on all tasks regardless of price.
- Under exponential demand, the optimal latecomer price is bounded by 1/b >= p* >= kappa_sigma(1) q.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Set price after observing the first firm's price | Late-deploying firm in the two-firm pricing game · Multi-task pricing game | revenue | Helped |
| Make task performance sufficiently similar across tasks | First-to-market firm · Two-task pricing game with exponential demand | revenue | Hurt |
| Differentiate model performance on at least one use case | First-to-market firm · Multi-task pricing game | revenue | Helped |
Surprising findings
- The first-to-market firm can obtain zero revenue regardless of its price when task performance differences are small relative to demand shares.
- The first-to-market firm benefits only if the competitor is incentivized to set high prices.
Limitations
- Assumes firms know user demand and competitor performance exactly; no noise.
- Static one-shot pricing ignores AI data flywheel effects.
- Excludes model development costs and build decisions.
Experimental setup
Metrics: firm revenue competitive ratio
Builds on: Stackelberg competition Bertrand competition
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