Governing Strategic Dynamics: Equilibrium Stabilization via Divergence-Driven Control

Black-box coevolution in mixed-motive games is often undermined by opponent-drift non-stationarity and noisy rollouts, which distort progress signals and can induce cycling, Red-Queen dynamics, and detachment. We propose the Marker Gene Method (MGM), a curriculum-inspired governance mechanism that stabilizes selection by anchoring evaluation to cross-generational marker individuals, together with DWAM and conservative marker-update rules to reduce spurious updates. We also introduce NGD-Div, which adapts the key update threshold using a divergence proxy and natural-gradient optimization. We provide theoretical analysis in strictly competitive settings and evaluate MGM integrated with evolution strategies (MGM-E-NES) on coordination games and a resource-depletion Markov game. MGM-E-NES reliably recovers target coordination in Stag Hunt and Battle of the Sexes, achieving final cooperation probabilities close to (1,1) (e.g., 0.991±0.01/1.00±0.00 and 0.97±0.00/0.97±0.00 for the two players). In the Markov resource game, it maintains high and stable state-conditioned cooperation across 30 seeds, with final cooperation of ≈ 0.954/0.980/0.916 in textscRich/textscPoor/textscCollapsed (both players; small standard deviations), indicating welfare-aligned and state-dependent behavior. Overall, MGM-E-NES transfers across tasks with minimal hyperparameter changes and yields consistently stable training dynamics, showing that top-level governance can substantially improve the robustness of black-box coevolution in dynamic environments.