A Short Note on: Optimal Control in Matching Pennies Game

This short note explores the application of optimal control theory in identifying mixed equilibrium strategies within the context of the Matching Pennies game. The study emphasizes the role of gradient descent as a fundamental mechanism in the players' learning dynamics. By formulating the game as an optimal control problem, the approach enables systematic analysis of strategic adaptation over time. In addition to the theoretical framework, simulation results are presented to illustrate and validate the effectiveness of the method in converging toward mixed equilibrium. The findings highlight the potential of control-theoretic techniques in advancing game-theoretic learning models.