Centipede Game

Imagine you can make a sure $2 bet on another’s person’s cooperation, and potentially make $100. What would it take for you to keep going after that $100?

The game works like this: players take turns, and each time they can either continue or end the game. If they continue, they gain a dollar. If they choose to stop, they keep their money and gain a dollar.

So at the first turn, Player 1 starts with $2, and can end it right there, and keep their $2. Or they can continue, and gain one. Player 2 starts with $1 but has the same continue/end options. And so it goes, up to 100. At the end, Player 2 makes the last move...does she honor and split the pot, $100 for both players...or defect, keeping $101 for herself and just $99 for the opponent?

The centipede game and the questions it poses is an example of game theory, as well as economic behavior. You’re trying to guess what people will do, so you start by looking at their potential gains/losses, and work backward from the end (backward induction). If the players can potentially make a lot at the end, why wouldn’t they just play until the end? The short answer: because they’re human, and humans are not always logical.

Some players might be more altruistic than others (meaning they tend to share with others), or self-preserving. Players might not all have the same understanding of long-term strategy, either...some might impulse grab and be done with it, even at just $50 before the other player screws them over. Some of it boils down to the perception the opponents have of one another. If you’re playing along and you think your opponent is such a twit they won’t see the benefit in waiting, you’ll end sooner than later before they do. Or, if you know the person and know they like to share, you’ll wait, counting on them to keep going, and benefit you both.