Gradient Descent Learning Matching the Pennies Repeated Game

An important game in teaching game theory is the matching the pennies. In this manuscript, some notes about this game are presented. This game has no pure Nash equilibrium and has mixing Nash \((0.5,0.5)\) . By maximizing expected return of each player, the optimal mixing portions are derived. Also, optimal expected return formulation is derived using a dynamic programming approach and ruin probability is studied.