The Theory of Strategic Evolution: Games with Endogenous Players and the Seven Laws of Strategic Replicators

Kevin Vallier

Papers from arXiv.org

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)

Date: 2025-12, Revised 2026-08
New Economics Papers: this item is included in nep-evo
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