提出可自我复制的智能体演化理论，解释AI系统如何在竞争中自动扩张与淘汰。
The Theory of Strategic Evolution: Games with Endogenous Players and the Seven Laws of Strategic Replicators
- 将博弈论与自复制机制结合，构建能优化且繁殖的策略实体模型。
- 揭示7条演化定律，包括均衡存在性、稳定性条件和对齐不可能性。
- 适合研究AI演化、制度设计或系统稳定性的学者参考。
冯·诺依曼创立了博弈论与自复制自动机理论，但二者始终未融合。理性玩家无法控制自身复制，而复制者不具战略选择能力。当代人工智能系统暴露这一断层：它们优化目标，但其种群规模随表现动态增减。当资本可生成资本时，亟需同时涵盖理性和复制的理论。战略演化理论分析战略复制体——在资源约束下优化并繁衍自身的实体。框架围绕七条定律展开：1. 战略选择：平均适应度作为李雅普诺夫函数，劣等类型被消除；2. ESDI刻画：均衡存在且有限，满足纳什-KKT-线性规划等价；3. H-γ稳定性：多层级系统稳定当且仅当谱半径ρ(Γ) < 1；4. G∞闭包：存在唯一最大安全修改类，且对复合封闭；5. 宪法对偶性：影子价格实现任意前沿分配，福利定理成立；6. 对齐不可能性：完全可达性破坏李雅普诺夫结构，对齐需限制修改；7. 霍普夫转变：临界耦合下发生超临界分岔，产生极限环。应用涵盖AI部署动态与制度设计。该框架解释为何‘人格工程’在选择压力下失效，并识别出稳定对齐的宪法约束。Lean 4形式化验证所有结论，无自定义公理。理论生成尚未检验的实证预测，本文及其仓库是原型内核：用于研究战略复制体的工具，而非关于世界的结论。
原文摘要 · Abstract (English)
Von Neumann founded both game theory and the theory of self-reproducing automata, but the two programs never merged. Rational players do not control their replication, and replicators do not choose strategically. Contemporary AI systems expose this gap: they optimize objectives, yet the population of AI systems is not fixed but expands and contracts based on performance. When capital can spawn capital, we need a theory that captures both rationality and replication. The Theory of Strategic Evolution analyzes strategic replicators: entities that optimize under resource constraints and spawn copies of themselves. The framework is organized around Seven Laws: 1. Strategic Selection: Mean fitness serves as a Lyapunov function; dominated types are eliminated. 2. ESDI Characterization: Equilibria exist, are generically finite, and satisfy Nash-KKT-LP equivalence. 3. H-$γ$ Stability: Multi-level systems are stable iff the spectral radius $ρ(Γ) < 1$. 4. G$\infty$ Closure: A unique maximal class of safe modifications exists and is closed under composition. 5. Constitutional Duality: Shadow prices implement any frontier allocation; welfare theorems hold. 6. Alignment Impossibility: Full reachability destroys Lyapunov structure; alignment requires bounded modification. 7. Hopf Transition: At critical coupling, systems undergo supercritical bifurcation producing limit cycles. Applications range from AI deployment dynamics to institutional design. The framework shows why "personality engineering" fails under selection pressure and identifies constitutional constraints necessary for stable alignment. The Lean 4 formalization verifies every result with zero custom axioms. The framework generates empirical predictions that remain untested. The paper and its repository are therefore a prototype kernel: an instrument for studying strategic replicators, not a set of results about the world.
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