# Governing Strategic Dynamics: Equilibrium Stabilization via Divergence-Driven Control

arXiv: https://arxiv.org/abs/2506.23734 · HTML: https://mlsanity.com/paper/2506.23734/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 50 references that are in the map.
- First posted on arXiv 30 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning](https://mlsanity.com/paper/1711.00832/) (2017)
- [The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization](https://mlsanity.com/paper/1807.03907/) (2018)
- [Proximal Learning With Opponent-Learning Awareness](https://mlsanity.com/paper/2210.10125/) (2022)
- [Fast Optimistic Gradient Descent Ascent (OGDA) method in continuous and discrete time](https://mlsanity.com/paper/2203.10947/) (2022)
- [Fast and Furious Symmetric Learning in Zero-Sum Games: Gradient Descent as Fictitious Play](https://mlsanity.com/paper/2506.13086/) (2025)
- [Coevolution and correlated multiplexity in multiplex networks](https://mlsanity.com/paper/1303.1369/) (2013)
- [Addressing Expensive Multi-objective Games with Postponed Preference Articulation via Memetic Co-evolution](https://mlsanity.com/paper/1711.06763/) (2017)
- [Coevolutionary Algorithm for Building Robust Decision Trees under Minimax Regret](https://mlsanity.com/paper/2312.09078/) (2023)
- [Cyclic dominance in evolutionary games: A review](https://mlsanity.com/paper/1408.6828/) (2014)
- [Coevolutionary intransitivity in games: A landscape analysis](https://mlsanity.com/paper/1501.04010/) (2015)
- [Beyond Nash Equilibrium: Achieving Bayesian Perfect Equilibrium with Belief Update Fictitious Play](https://mlsanity.com/paper/2409.02706/) (2024)
- [Approximating Nash Equilibria in General-Sum Games via Meta-Learning](https://mlsanity.com/paper/2504.18868/) (2025)

## Abstract (arXiv)

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.