# Safe Equilibrium Policy Optimization for Strategic Agent Policies

arXiv: https://arxiv.org/abs/2605.30854 · HTML: https://mlsanity.com/paper/2605.30854/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 23 of its 37 references that are in the map.
- First posted on arXiv 29 May 2026.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 23 of 23)

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- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning](https://mlsanity.com/paper/1711.00832/) (2017)
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- [Deal or No Deal? End-to-End Learning for Negotiation Dialogues](https://mlsanity.com/paper/1706.05125/) (2017)
- [Improving Language Model Negotiation with Self-Play and In-Context Learning from AI Feedback](https://mlsanity.com/paper/2305.10142/) (2023)
- [Decoupling Strategy and Generation in Negotiation Dialogues](https://mlsanity.com/paper/1808.09637/) (2018)
- [Deep Reinforcement Learning from Self-Play in Imperfect-Information Games](https://mlsanity.com/paper/1603.01121/) (2016)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [Inequity aversion improves cooperation in intertemporal social dilemmas](https://mlsanity.com/paper/1803.08884/) (2018)
- [Deep Counterfactual Regret Minimization](https://mlsanity.com/paper/1811.00164/) (2018)
- [Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4](https://mlsanity.com/paper/2309.17277/) (2023)
- [Computing Approximate Equilibria in Sequential Adversarial Games by Exploitability Descent](https://mlsanity.com/paper/1903.05614/) (2019)
- [K-Level Reasoning: Establishing Higher Order Beliefs in Large Language Models for Strategic Reasoning](https://mlsanity.com/paper/2402.01521/) (2024)

## Abstract (arXiv)

Language models fine-tuned with reinforcement learning typically optimize for task reward, ignoring multi-agent strategic structure. Because these agents condition on natural language game-state descriptions and emit actions through free-form generation, strategic failure modes -- exploiting weaker opponents, coordinating on harmful equilibria, and externalizing costs are inseparable from the language interface itself. We propose Safe Equilibrium Policy Optimization (sepo), a training objective that augments expected payoff with explicit penalties for exploitability, collusion risk, and externality cost. We implement sepo as a reward signal for Group Relative Policy Optimization (GRPO), applied to Gemma~4 E4B-it and Qwen~3.5-4B after supervised fine-tuning (SFT). Evaluated across five strategic domains: Iterated Prisoner's Dilemma, repeated auctions, two negotiation variants, and Kuhn Poker. sepo achieves zero exploit-pool advantage in Kuhn Poker for both models, outperforms the base model on safety in four domains, and corrects the over-cooperative behavior introduced by SFT. In negotiation, sepo achieves a positive-safety outcome and only the positive normalized relative advantage of any negotiation configuration. Ablation experiments confirm that per-rollout exploit computation is necessary: a shared constant penalty cancels in GRPO advantage normalization (constant control-variate property), producing zero gradient. To support further research in strategic safety for agents, we release our hrefhttps://anonymous.4open.science/r/sepo-2668/README.mdcode and SFT datasets.