Definition of 'Centipede Game'
An extensive-form game in game theory in which two players alternately get a chance to take the larger share of a slowly increasing money stash. The Centipede Game concludes as soon as a player takes the stash, with that player getting the larger portion and the other player getting the smaller portion. While not as well-known as the famed Prisoner’s Dilemma, the Centipede Game also highlights the conflict between self-interest and mutual benefit with which people have to grapple. It was first introduced by psychologist Robert Rosenthal in 1982. “Centipede Game” is so-called because its original version consisted of a 100-move sequence, and the payoff diagram detailing it looked like a centipede.
Investopedia explains 'Centipede Game'
As an example, consider the following version of the Centipede Game involving two players, Jack and Jill, who are playing for a total stash of $100. The game starts with a $2 payoff; Jack goes first, and has to decide if he should "take" the payoff or "pass." If he takes, then he and Jill both get $1 each, but if he passes, the decision to “take or pass” now must be made by Jill. The payoff is now increased by $1 to $3; if Jill takes, she gets the full $3 and Jack gets $0, but if she passes, Jack gets to decide whether to take or pass. If she passes, the payoff is increased by $1 to $4; if Jack takes, the stash is split equally at $2 each. If he passes and Jill takes, the payoff of $5 would be split as follows – Jill $4, Jack $1. The game continues in this vein for a total of 99 rounds. If both players always choose to pass, they each receive a payoff of $50 at the end of the game. Note that the money is contributed by a third party and not by either player.
What does game theory predict? Using backward induction – which is the process of reasoning backward from the end of a problem – game theory predicts that Jack (or the first player) will choose to take on the very first move and both players will receive a $1 payoff.
In experimental studies, however, only a very small percentage of subjects chose to take on the very first move. This discrepancy can be explained by a couple of reasons. One reason is that some people are altruistic, and would prefer to cooperate with the other player by always passing, rather than taking down the pot. Another reason is that people may simply be incapable of making the deductive reasoning necessary to make the rational choice predicted by the Nash equilibrium. The fact that few people take the stash on the very first move is not too surprising, given the small size of the starting payoff when compared with the increasing payoffs as the game progresses.