This is a Visualization of the Centipede Game in Game Theory. There are two players switching turns and by continuing they increase the payoff but also the chance the other player quits for getting a better payoff. The name "Centipede" comes from the graph you can draw for the possible payoffs of each player.
Broader Game Theory Introduction:
Let's Play!
On the following page two persons or one person and a computer can play the game. Player 1 can choose first if to continue or end the game, then it's player 2's turn. It continues till one of the players is ending the game or the last round is reached. The graph shows the possible payoffs for each player and the current state of the game.
Based on Backwards Induction the best play for the first player is to quit on the first round, if they expect, the game won't continue till the end. But more money, a longer game or social thoughts can change the perception of what is desirable.
Choose one of the buttons to play either the simple version of the Game or a version with the Centipede Graph with 2 human players. The third button lets you play against a computer player.