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

Research from arXiv introduces the Theory of Strategic Evolution, which merges game theory with the theory of self-reproducing automata. This theory proposes 'strategic replicators' as entities that optimize resources and self-replicate, introducing 'Games with Endogenous Players' (GEPs) where strategic units are lineages, not individual instances. The equilibrium concept is defined as Evolutionarily Stable Distributions of Intelligence (ESDIs). The mathematical framework involves a hierarchy of strategic layers linked by cross-level gain matrices, which, under a small-gain condition, allows for a global Lyapunov function.

Why it matters

This research provides a novel theoretical framework for understanding systems where entities not only strategize but also evolve and self-replicate. It could offer new insights into complex adaptive systems, competition, and the emergence of stability in dynamic environments. Such a framework has the potential to influence strategic planning and risk assessment in domains characterized by evolving agents and resource competition.

Key insights

• The Theory of Strategic Evolution synthesizes game theory and self-reproducing automata.
• Strategic replicators are defined as resource-optimizing and self-replicating entities.
• Games with Endogenous Players (GEPs) consider lineages as fundamental strategic units.
• Evolutionarily Stable Distributions of Intelligence (ESDIs) serve as the equilibrium concept in GEPs.
• The mathematical model uses a hierarchy of strategic layers with cross-level gain matrices.
• A global Lyapunov function is present under a small-gain condition (spectral radius less than one).

Source

arXiv — Computers and Society — https://arxiv.org/abs/2512.07901