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Braess’s Paradox of Generative AI
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Models GenAI's revenue-maximizing training schedule against a human forum with network effects, showing optimal schemes can be non-cyclic, socially harmful (Braess-like paradox), with unbounded price of anarchy, and deriving regulator conditions for social benefit.
Problem
Long-term social impact of generative AI (GenAI) that competes with human-based Q&A forums (e.g., Stack Overflow) whose network effects weaken as users shift to GenAI, and how a regulator with incomplete information can ensure GenAI is socially beneficial.
Approach
A sequential game model where GenAI strategically chooses training rounds, users follow a softmax over utilities from GenAI (decaying with time since last training) and a forum with network effects; it shows revenue-optimal training can be socially harmful (Braess-like), and derives necessary and sufficient regulator conditions based on bounding user proportions.
Key results
- Proposes an approximation algorithm (O(T^2/epsilon) time) for GenAI's revenue-maximizing training scheme, showing optimal schemes need not be cyclic; cyclic schemes are Theta(1) suboptimal in the example.
- Shows a Braess-like paradox: the revenue-optimal/optimal training scheme can be socially harmful, with users better off without GenAI.
- Proves the price of anarchy is unbounded: for every M there is an instance with PoA > M.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the revenue-maximizing training scheme instead of removing GenAI | GenAI–Forum ecosystem · Some model instances | social welfare | Hurt |
| allow GenAI to compete with the Forum | GenAI–Forum ecosystem · Some model instances | social welfare | Hurt |
| use sparse training rather than frequent training | GenAI · Long-term user welfare | social welfare | Hurt |
| use a non-cyclic training scheme rather than any cyclic training scheme | GenAI revenue maximization, Example instance · Example instance, sufficiently large T | average revenue: Θ(1) | Helped |
| train every round rather than use the revenue-maximizing no-training scheme | GenAI, constructed Price of Anarchy instance · Constructed instance | social welfare | Helped |
| increase the initial proportion of users choosing GenAI | GenAI–Forum user dynamics · Any fixed instance and training scheme | GenAI user proportion | Helped |
Surprising findings
- Cyclic training schemes, which seem natural, can be highly suboptimal for revenue, while non-cyclic schemes do better.
- GenAI's presence can make all users worse off than a world with only the human forum, despite GenAI being better in the short term.
Limitations
- Results hold only for restricted parameter regimes (e.g., beta*L < 16/7) for the contraction-based analysis.
- Forum is modeled as non-strategic.
- Purely theoretical model with stylized utility and softmax user behavior; no empirical validation with real users.
Experimental setup
Metrics: social welfare revenue price of anarchy
Baselines: no-training scheme cyclic training schemes welfare-maximizing scheme (train every round)
Builds on: Braess's paradox Tullock contest price of anarchy
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