centipede - In the game of centipede players take turns...

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In the game of centipede, players take turns making moves on a centipede board, trying to maximize their own score over the match. 5 or more of these games will constitute a match, with players alternating their positions (who makes the first move) each game. In each game, player one begins with a choice to end the game and give each player zero points, or to let player two make a choice. Player two's choice is between giving themselves 35points and taking 25 points away from player 1. If player two chooses to continue the game, the choice is between continuing and giving 10 points to each player. Player two's second choice is between 45 points for themselves and -15 points for player one, and 20 points for each player. After each game, the people playing will switch between player one and player two, and play another game. After the fifth game, and each game after that, the match has a .25 chance of ending, based on a series of coin flips. In our game, we began by following the strategy prescribed by the standard theory of rational choice for two rounds. However, after we played two rounds, we began trying to work towards a collaborative strategy that would net the most points over the match. Despite an instance of a "revenge" move, and the event that preceded it, we ended up with 40 points each over 6 games. If the match were to have continued for longer, we would have been settled on the most productive collaboration strategy, netting us both 20 points each game. The standard
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