

Centipede Game 
The centipede game was first introduced by Rosenthal (1982) and has subsequently been studied by Binmore(1987), Kreps (1990) Reny (1988) and many others in different modified forms. The original version of the game consisted of a sequence of a hundred moves (hence the name centipede) with linearly increasing payoffs. 
Description 
The centipede game is an extensiveform game in which two players alternately get a chance to take the larger portion of a contiually increasing pile of money. As soon as a player takes, the game ends with that player getting the larger portion of the pile while the other player gets the smaller portion. Passing strictly decreases a player?s payoff if the opponent takes on the next move. If the opponent also passes, the two players are faced with the same choice situation with reversed roles and increased payoffs. The game has a finite number of moves which is known in advance to both players. 
In the above diagram, a 1 at a black circle ("decision node") denotes a decision opportunity for player 1. A 2 at a decision node tells us that person 2 can make a decision here. The top number at the end of each vertical line is a payoff for player 1 and the bottom number is a payoff for player 2.Player 1 has the first move: if she chooses D, both players get 1; if she chooses A, the opportunity to make a decision passes to player 2. Player 2 has the second move: if he chooses D, player 1 gets payoff of D and he gets 3; if he chooses A, the opportunity to make a decision passes to player 1. And so on to the end of the game tree. If both players always choose A, they both receive payoff of 100 at the end of the game tree. 
Theoretical Predictions 
We have just observed that both players receive payoff of 100 if both players always choose A rather than D. Note also that both players receive payoff of 1 if player 1 chooses D on his first move. 
Typical Experimental Results 
Studying actual behaviour in different versions ( a four move, six move, and high payoff versions) of the centipede game, McKelvey and Palfrey (1992) found that subjects rarely followed the theoretical predictions. In fact in only 7% of the fourmove games, 1% of the sixmove games, and 15% of the high payoff games did the first player choose to take on the first move. Similar results were reported by Nagel and Tang (1998). 
Possible Explanations of "Irrational" Behavior 
There are two types of explanation to account for the divergence. The first assumes that the subject pool contains a certain proportion of altruists who place a positive weight in their utililty function on the payoff of their opponent. Also to the extent that selfish players believe that there is some probability that other players are altruistics, they have an incentive to mimic altruistic behaviour by passing. The second explanation considers the possibility of action errors. Errors in action, or ?noisy? play, may result from subjects experimenting with different strategies. Or simply from subjects pressing the wrong key. 
Available Software 
More Discussions on Variants of the Centipede Game 
Binmore,K. & McCarthy,J. & Ponti,G. & ..., (1999). "A backward induction experiment," Working papers 34, University of Wisconsin Madison  Social Systems

References 
R.McKelvey and T.Palfrey (1992) ? An experimental study of the centipede game,? Econometrica 60 

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