Centipede

The centipede game is an extended form game in game theory that was initially developed by Robert Rosenthal in 1981. Two players alternately choose to accept a slightly greater portion of a growing pot or to pass the pot to the other player. The payoffs are set up so that if one hands the pot to an opponent and that opponent wins it on the following round, one receives a little less money than if one had won it on this round, but the potential payout will be bigger after another switch. Consequently, even if a player has a motive to grab the pot at every round, it would be best for them to wait.

Any game having this structure but a variable number of rounds is referred to as a centipede game, even though the original centipede game had a cap of 100 rounds (thus the name). The first player to take the pot on the first round of the game occurs in the only subgame perfect equilibrium (and in every Nash equilibrium) of these games. However, in empirical tests, relatively few players take the pot, leading to a bigger payout than in the subgame perfect and Nash equilibria. These findings are interpreted to demonstrate that in some situations, subgame perfect equilibria and Nash equilibria are unable to forecast human play. In introductory game theory courses and literature, the Centipede game is frequently used to emphasize the ideas of backward induction and the iterative removal of dominated tactics, which demonstrate a popular method of supplying a solution to the game.