Centipede game:-

The two-player game in Figure 1 is known as a "centipede game" because of its shape. (The game, like the arthropod, may have fewer than 100 legs.)

The players move alternately; on each move a player can stop the game (S) or continue (C). On any move, a player is better off stopping the game than continuing if the other player stops immediately afterwards, but is worse off stopping than continuing if the other player continues, regardless of the subsequent actions.

After k periods, the game ends. This game has a finite horizon, so we may find its subgame perfect equilibria by using backward induction. The last player to move prefers to stop the game than to continue.

Given this player's action, the player who moves before her also prefers to stop the game than to continue. Working backwards, we conclude that the game has a unique subgame perfect equilibrium, in which each player's strategy is to stop the game whenever it is her turn to move. The outcome is that player 1 stops the game immediately.