Played By the System: Chaotic Games and the Death of Foresight

The study of game theory focuses on games between players which may be anything from individuals, businesses, governments, or competing populations of animals. Each player has a set of n moves {E1, E2, . . . , En} from which they form a strategy. These are either pure strategies in which a player always plays one move, or mixed strategies de ned as a probability distribution over their moves, in which players randomly decide between their moves according to the distribution. What each player gains or loses given their move and the moves of the other players is held as a matrix. As the example this paper will mainly focus on, we look to Rock, Paper, Scissors(RPS). RPS is played by 2 players A and B, both of which share a moveset {Rock, Paper, Scissors}. Their payo s are held by the payo matrices A for Alice and B for Bob, where