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Market Incentives for AI Safety Investment
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Game-theoretic model of safety investment in an AI supply chain (upstream LLM provider, Cournot downstream firms, Nash-in-Nash fee bargaining) deriving market-driven safety levels and regulatory effects.
Problem
How profit maximization shapes safety investment by an upstream LLM provider and competing downstream firms, and how that compares with welfare- and industry-profit-optimal levels, and how regulation changes incentives.
Approach
Combines Cournot competition with quasilinear consumer utility, Nash-in-Nash bargaining over access fees, and neural-scaling-law-based safety costs to derive closed-form safety investment levels; finds downstream competition induces more firm safety investment than industry-profit optimum, while the provider may underinvest due to incomplete capture of surplus.
Key results
- Downstream competition generally induces firms to invest more in safety than the industry-profit-optimal level (Proposition 5.3 comparison with market-driven levels).
- Upstream provider may underinvest relative to industry-profit and welfare benchmarks because it is not fully compensated for the surplus its safety investments create.
- Strict downstream or upstream regulation raises safety investment levels but reduces participants' profits and may cause provider exit.
Surprising findings
- Overly fierce downstream competition can lower cumulative safety, since the equilibrium investment levels decrease in competition intensity for large gamma and firm count.
- Under the model, the provider may invest enough that firms make zero investment when the number of firms is large, due to positive externality.
Limitations
- Assumes symmetric firms, which may not hold with horizontal differentiation.
- Excludes catastrophic risks; focuses on lower-impact errors described by scaling laws.
- Relies on absence-of-disruption assumption and perfect regulatory enforcement.
Experimental setup
Metrics: safety investment level industry profit market welfare provider profit
Baselines: Laufer et al. (2025) model industry-profit-optimal investment market-welfare-optimal investment
Builds on: Cournot competition (Dixit, 1979) Nash-in-Nash bargaining (Collard-Wexler et al., 2019) Tsoy and Konstantinov (2023) Laufer et al. (2025) Gordon and Loeb (2002)
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