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

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  • Kevin Vallier

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.

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  • Kevin Vallier, 2025. "The Theory of Strategic Evolution: Games with Endogenous Players and Strategic Replicators," Papers 2512.07901, arXiv.org, revised Dec 2025.
    • Handle: RePEc:arx:papers:2512.07901
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    1. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
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