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

TL;DR

This paper synthesizes game theory and automata theory to analyze strategic evolution with endogenous players, introducing a hierarchical framework and stability conditions applicable to AI, markets, and institutions.

Contribution

It introduces Games with Endogenous Players and the concept of Evolutionarily Stable Distributions of Intelligence, merging strategic automata with evolutionary game theory.

Findings

Global Lyapunov functions exist under small-gain conditions

Closure under meta-selection preserves dynamical structure

Unrestricted self-modification can destabilize systems

Abstract

Von Neumann founded both game theory and the theory of self-reproducing automata, but the two programs never merged. This paper provides the synthesis. The Theory of Strategic Evolution analyzes strategic replicators: entities that optimize under resource constraints and spawn copies of themselves. We introduce Games with Endogenous Players (GEPs), where lineages (not instances) are the fundamental strategic units, and define Evolutionarily Stable Distributions of Intelligence (ESDIs) as the resulting equilibrium concept. The central mathematical object is a hierarchy of strategic layers linked by cross-level gain matrices. Under a small-gain condition (spectral radius less than one), the system admits a global Lyapunov function at every finite depth. We prove closure under meta-selection: adding governance levels, innovation, or constitutional evolution preserves the dynamical structure. The Alignment Impossibility Theorem shows that unrestricted self-modification destroys this structure; stable alignment requires bounded modification classes. Applications include AI deployment dynamics, market concentration, and institutional design. The framework shows why personality engineering fails under selection pressure and identifies constitutional constraints necessary for stable multi-agent systems.