Fractal Games

Abstract

This study introduces Fractal Games, a game-theoretic framework designed to formalize hierarchical recursion within noncooperative antagonistic systems. Traditional equilibrium models capture only local stability, overlooking how stress accumulates and amplifies across layers. The framework establishes sufficient conditions under which lower-level boundary equilibria persist upward as internal stress, leading to endogenous acceleration and a cascading collapse without the need for external shocks. By linking static persistence to dynamic amplification, the model demonstrates how hierarchy alone can reshape the set of feasible equilibria and induce fundamental structural bifurcations. Numerical simulations successfully reproduce these effects and identify four key control levers that mitigate upward propagation: cross-cost relief, stress-saturation caps, weight diversification, and defender incentives. Collectively, these findings offer a unified and rigorous account of how hierarchical organization can transform local balance into system-wide failure, and how targeted interventions can effectively stabilize hierarchical systems.