Minimax Value Iterarion Applied to Robotic Soccer

This work focuses on developing a dynamic programming algorithm to solve a class of Stochastic Games called two-person zero-sum games, inspired by the reinforcement learning algorithm Minimax-Q. In each state of the game, linear programming is used to find a Nash equilibrium, which ensures optimality in a worst-case scenario. The method is then applied to a behavioral model of a robotic soccer game. The goal is to find the worst case scenario strategy for such a team, so that a lower bound for the team’s performance is guaranteed. Most of the times it converges to a conservative solution that tries, above all, to keep the opponent from scoring, rather than trying to score itself.