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 res...