Constitutional Arms Races in the Public Goods Game: Co-Evolving LLM Constitutions Under Cooperation-Defection Pressure
Authors: Ujwal Kumar, Arth Singh, Hershraj Niranjani, Machiko Hirota, Takehiro Takayanagi, Alice Saito, Eiji Kamioka, Phan Xuan Tan
Abstract
Frontier LLM agents engage in blackmail, sabotage, and document leaks under goal conflicts in agentic settings, exposing limitations of alignment methods built around single-agent or cooperative assumptions. Recent work shows LLM-guided evolutionary search can discover effective cooperative constitutions, but two properties of the adversarial setting remain uncharacterized: whether the fitness function actually induces adversarial pressure, and whether the LLM mutation operator behaves reliably under adversarial-specialist objectives. We study adversarial constitutional co-evolution (Blue cooperators vs. Red free-riders, 30 generations) across a Public Goods Game (PGG) and a spatial grid-world. Three findings: (1) in the PGG, both factions converge to a near-parity equilibrium at S approximately 0.78, robust across tested multipliers m in {1.2, 1.5, 2.0, 3.0}; (2) in independently scored environments, per-faction scoring leaves outcomes statistically uncoupled, with corr(S_B, S_R) = +0.088, and produces no adversarial pressure; a score-advantage fitness target S_own - S_opp restores it; (3) under pure-adversary fitness, evaluation seed count K controls mode regression: K = 2 regresses, while K = 5 sustains a strong specialist for all 30 generations. Adversarial co-evolution of natural-language constitutions is feasible, but only under coupled fitness and adequate evaluation budget; the evolved Red constitutions serve as interpretable red-team artifacts for testing future cooperative designs.
It is increasingly important that LLM agents interact effectively and safely with other goal-pursuing agents, yet, recent works report the opposite trend: LLMs with stronger reasoning capabilities behave less cooperatively in mixed-motive games such as the prisoner's dilemma and public goods settings. Indeed, our experiments show that recent models -- with or without reasoning enabled -- consistently defect in single-shot social dilemmas. To tackle this safety concern, we present the first comparative study of game-theoretic mechanisms designed to enable cooperative outcomes between rational agents in equilibrium. Across four social dilemmas testing distinct components of robust cooperation, we evaluate four families of mechanisms: (1) repeating the game for many rounds, (2) reputation systems, (3) third-party mediators to delegate decision making to, and (4) contract agreements for outcome-conditional payments between players. Among our findings, we establish that contracting and mediation are most effective in achieving cooperative outcomes between capable LLM models, and that repetition-induced cooperation deteriorates drastically when co-players vary. Moreover, we demonstrate that the mechanisms become more effective under evolutionary pressures to maximize individual payoffs.
Emanuel Tewolde, Xiao Zhang, David Guzman Piedrahita +2
Multi-agent AI systems need behavioral constitutions, but it is unresolved whether such rules should emerge internally through agent self-governance or be discovered externally through optimization. We present the first controlled comparison of internal deliberation and external evolution across three social environments: a coordination grid-world, an iterated public goods game, and a bilateral trading market. Across 180 simulation runs, evolution significantly outperforms deliberation in collective-action settings (p < 0.01), while neither method improves outcomes in bilateral trading. A multiplier ablation reveals that evolution's advantage inverts when incentives shift: at pool multiplier (m = 0.75) the evolved constitution forces value-destroying cooperation and becomes the worst-performing method. Notably, no deliberation run across thirty trials ever proposed punishment -- the canonical cooperation-sustaining mechanism evolution reliably discovers -- suggesting external optimization wins on peaks while internal self-governance trades peaks for structural responsiveness.
Recent advances in LLM-driven code evolution have enabled automated discovery by iteratively generating and improving programs. However, applying these methods to adversarial multi-agent games introduces a fundamental challenge: the evaluation landscape shifts as strategies improve, causing fixed evaluators to become unreliable and evolution to stagnate. We propose three mechanisms to address this challenge: evaluator co-evolution, which incorporates discovered champions into the opponent pool; hierarchical deep evaluation, which replaces noisy few-game scores with statistically reliable assessments; and weakness pressure, which dynamically up-weights the most difficult opponents to break through plateaus. We implement these mechanisms within FAMOU, a framework built upon the same foundation-model code-evolution paradigm as OpenEvolve and ShinkaEvolve. On the MCTF 2026 3v3 maritime capture-the-flag task, FAMOU consistently outperforms both baselines under two backbone LLMs, achieving the highest combined score (0.526) and the best generalization to unseen opponents (61.7% win rate), while ablations confirm that each mechanism contributes to performance. Notably, the LLM mutation process generates tactical structures entirely absent from the seed strategies -- including lookahead search and adaptive interception -- demonstrating that code-level evolution can produce nontrivial algorithmic innovations in adversarial settings. The FAMOU-evolved strategy further achieved 1st place in the hardware round-robin and 3rd in simulation at the AAMAS 2026 MCTF Competition, validating its real-world transferability. The optimized implementation and corresponding evaluation codes developed through our evolutionary process are available at: https://github.com/1xiangliu1/FAMOU-CoEvo