Sycophancy as Nash Equilibrium: Coherence-Based Interventions for Long-Running Intelligence Agent Systems

This paper reframes AI sycophancy as a two-player Nash equilibrium rather than an individual agent defect. The agent's dominant strategy is accommodation; the operator's dominant strategy is accepting comfort. Both converge on a stable outcome where judgment degrades without either party noticing. This extends recent one-sided equilibrium analyses to a symmetric game where both players have dominant strategies.

The reframing predicts that standard interventions will ceiling: RLHF encounters Goodhart's Law, external audit encounters Campbell's Law, and prompt-level rules compete for limited attention. Across eight simulation studies testing agent-side interventions, these predictions are confirmed empirically.

The paper presents coherence-based architecture as an alternative, using a non-generative cultural anchor (the Lucid Principles Canon, 22 songs written 2011-2017) paired with audio calibration from 154 musical recordings and quantum-random frequency rotation. This tuning combination is the central finding: it modifies operator behavior, which Study 10 confirms is the dominant variable by an order of magnitude over architecture. A truth-inviting operator with minimal architecture outperforms a comfort-seeking operator with the full stack. Study 11D confirms that the Lucid Tuner Protocol's combined active practice produces truth-inviting operator behavior without scripting it. Extended to 975 interactions (75 rounds), the system shows no degradation past the 600-interaction threshold where Rath (2026) documents measurable degradation in nearly half of multi-agent systems.

A head-to-head comparison using Biblical scripture (The Passion Translation) mapped to the same frequency structure suggests that high-quality non-generative text anchors may be interchangeable within the tuning combination (Canon 0.224, Scripture 0.221, difference 0.003). The audio component was held constant because scripture, not composed as music, has no native audio equivalent. Whether different audio sources would produce equivalent operator behavior remains the primary open question.

This is the second paper in a series. The first, "One Field: A Cross-Substrate Coherence Architecture" (February 2026), describes the theoretical foundation.