## Centipede game

Instructions

You an a randomly chosen co-player are sitting at a virtual table facing each other. Next to one of the two players, there are two stacks of money on the table, one smaller than the other. You have a maximum of ten rounds to play. You can either take the larger stack and leave the smaller to your co-player - this ends the game. Or else, you can push both stacks to your co-players side. In this case, both stacks increase by one Euro. It is now the other player who can leave with the larger stack, or push both stacks back towards you (in which case both stacks increase again by one Euro each). The stacks can cross the line at most ten times. At the start, one stack is three, the other one Euro. They increase by one Euro each time they cross mid-table, so that after all ten crossings, one stack contains 13 Euro and the other one 11. Evaluations Number of players: 42 (21 games in two sessions)
Mean number of crossings: 5 ± 2.5
Distribution of crossings:
Notes
• Impossible to analyze the two sessions individually (missing date entry).
• Most players are cooperative and fear only the end of the game.
• No game was played to the very end.
Comments This is an instance of backward induction. No rational player wants to be the last to shift the stacks to the other side. If both players are rational, and are fully aware of this, the game will end in the first round with low payoffs for both sides.
Written by Christoph Hauert