The Centipede Game is a well known game involving two players. For some finite number of turns the players alternate choosing between two options: “take” or “pass.” The first player that chooses “take” ends the game, wins the game, and also gets a reward. Otherwise, if each player chooses “pass” for every turn in the game, the game will end and both players get some reward.

The longer the game goes on, the higher the reward becomes for the players if they decide to “take.” So the question is, what is the best turn for a player to “take?”

The standard game theoretic approach involving subgame perfect Nash equilibria (SPNE’s) predicts that the optimal strategy for both players is to immediately “take” in the first turn. The goal of this paper is to create several different machine learning models that both play and learn the Centipede Game, and then compare what the models predict is the best turn to “take” versus what the game theoretic results predict.