Artificial Intelligence · 11.08.2026, 14:25 UTC
The Theory of Strategic Evolution: Games with Endogenous Players and the Seven Laws of Strategic Replicators
| Schweregrad | info |
|---|---|
| Kategorie | Artificial Intelligence |
| Quelle | arXiv cs.AI ↗ |
| Veröffentlicht | 11.08.2026 UTC |
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arXiv:2512.07901v4 Announce Type: replace-cross Abstract: 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-$\gamma$ Stability: Multi-level systems are stable iff the spectral radius $\rho(\Gamma) < 1$. 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 …