Chaotic time series prediction for the game, Rock-Paper-Scissors

Two players of Rock-Paper-Scissors are modeled as adaptive agents which use a reinforcement learning algorithm and exhibit chaotic behavior in terms of trajectories of probability in mixed strategies space. This paper demonstrates that an external super-agent can exploit the behavior of the other players to predict favorable moments to play against one of the other players the symbol suggested by a sub-optimal strategy. This third agent does not affect the learning process of the other two players, whose only goal is to beat each other. The choice of the best moment to play is based on a threshold associated with the Local Lyapunov Exponent or the Entropy, each computed by using the time series of symbols played by one of the other players. A method for automatically adapting such a threshold is presented and evaluated. The results show that these techniques can be used effectively by a super-agent in a game involving adaptive agents that exhibit collective chaotic behavior.