Feedback Linearization for Replicator Dynamics: A Control Framework for Evolutionary Game Convergence

This paper demonstrates the first application of feedback linearization to replicator dynamics, driving the evolution of non-convergent evolutionary games to systems with guaranteed global asymptotic stability. Replicator dynamics, while a cornerstone of evolutionary game theory, possess neutral stability at Nash equilibria [2], which causes the evolutionary process to oscillate without converging to an optimal strategy. We build a control-theoretic framework that cancels the nonlinear components in replica-tor dynamics, and then apply a linear feedback component to force a strategy change at the Nash equilibrium. Through Lyapunov analysis, we show global convergence from any initial conditions in the probability simplex. We illustrate this approach with a numerical example of a penalty shootout game, where we illustrate that our method guides strategies quickly to mixed Nash equilibria, while the uncontrolled dynamics oscillate. Our work serves as one of the first known connections between nonlinear control theory and evolutionary game dynamics with applications in multi-agent systems, algorithmic trading, and strategic optimization.