Reward Hacking as Equilibrium under Finite Evaluation

We prove that under five minimal axioms -- multi-dimensional quality, finite evaluation, effective optimization, resource finiteness, and combinatorial interaction -- any optimized AI agent will systematically under-invest effort in quality dimensions not covered by its evaluation system. This result establishes reward hacking as a structural equilibrium, not a correctable bug, and holds regardless of the specific alignment method (RLHF, DPO, Constitutional AI, or others) or evaluation architect

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ethics.ai (30 March 2026), “Reward Hacking as Equilibrium under Finite Evaluation,” evidence record 6605, https://ethics.ai/record/6605 (originally published by arXiv).

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