What Is the Centipede Game?
The centipede game is an extensive-form game in game thought right through which two avid players alternately get a possibility to take the larger percentage of a slowly emerging money stash. It is arranged so that if a player passes the stash to their opponent who then takes the stash, the player receives a smaller amount than if that that they had taken the pot.
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. The game has a predefined total number of rounds, which can also be known to every player in advance.
Key Takeaways
- The centipede game is a game right through which two avid players exchange to take a percentage of an ever-increasing amount of cash.
- It is an forefront technique to the warfare between self-interest and mutual benefit.
- Inside the distinctive fashion of the centipede game, the avid players take turns deciding whether or not or to not assert the larger percentage of an ever-increasing pot.
- In most diversifications, the centipede game terminates after a suite number of rounds, providing an incentive for avid players to complete the game.
- Even supposing game thought signifies that self-interested avid players must end the game early, real-life trials in most cases have a tendency to continue for longer than expected.
Understanding the Centipede Game
While not as widely known since the famed Prisoner’s Catch 22 situation, the centipede game moreover highlights the warfare between self-interest and mutual benefit with which people wish to grapple. It was first introduced by means of economist Robert W. Rosenthal in 1982. The “centipede game” is so-called on account of its distinctive fashion consisted of a 100-move assortment.
For example, imagine the following fashion of the centipede game involving two avid players, Jack and Jill. The game starts with an entire $2 payoff. Jack goes first, and has to decide if he must “take” the payoff or “move.” If he’s taking, then he’ll get $2 and Jill gets $0, but if he passes, the decision to “take or pass” now must be made by means of Jill. The payoff is now upper by means of $2 to $4; if Jill takes, she’s going to get $3 and Jack gets $1, but if she passes, Jack gets to decide whether or not or to not take or move. If she passes, the payoff is upper by means of $2 to $6; if Jack takes, he would get $4, and Jill would get $2. If he passes and Jill takes, the payoff will build up by means of $2 to $8, and Jack would get $3 while Jill got $5.
The game continues in this vein. For every round n, the avid players take turns deciding whether or not or no longer or not to claim the prize of n+1, leaving the other player with a reward of n-1.
If every avid players always select to head, the game continues until the only centesimal round, when Jill receives $101 and Jack receives $99. Since Jack would have received $100 if he had ended the game at the 99th round, he would have had a financial incentive to complete the game earlier.
What does game thought be expecting? Using backward induction—the process of reasoning backward from the highest of a topic—game thought predicts that Jack (or the main player) will select to take on the very first flow and procure a $2 payoff.
In experimental analysis, on the other hand, only a very small percentage of subjects decided on to take on the very first flow. This discrepancy can have a variety of explanations. One the explanation why is that some individuals are altruistic, and wish to cooperate with the other player by means of always passing, reasonably than taking down the pot.
Another reason is that folks would in all probability simply be incapable of making the deductive reasoning essential to make the rational variety predicted by means of the Nash equilibrium. The fact that few other people take the stash on the very first flow is not too surprising, given the small size of the start payoff compared with the emerging payoffs as the game progresses.
