DEFINITION of 'Centipede Game'

An extensive-form game in game theory in which two players alternately get a chance to take the larger share of a slowly increasing money stash. The Centipede Game concludes as soon as a player takes the stash, with that player getting the larger portion and the other player getting the smaller portion. While not as well-known as the famed Prisoner’s Dilemma, the Centipede Game also highlights the conflict between self-interest and mutual benefit with which people have to grapple. It was first introduced by psychologist Robert Rosenthal in 1982. “Centipede Game” is so-called because its original version consisted of a 100-move sequence, and the payoff diagram detailing it looked like a centipede.

BREAKING DOWN 'Centipede Game'

As an example, consider the following version of the Centipede Game involving two players, Jack and Jill, who are playing for a total stash of $100. The game starts with a $2 payoff; Jack goes first, and has to decide if he should "take" the payoff or "pass." If he takes, then he and Jill both get $1 each, but if he passes, the decision to “take or pass” now must be made by Jill. The payoff is now increased by $1 to $3; if Jill takes, she gets the full $3 and Jack gets $0, but if she passes, Jack gets to decide whether to take or pass. If she passes, the payoff is increased by $1 to $4; if Jack takes, the stash is split equally at $2 each. If he passes and Jill takes, the payoff of $5 would be split as follows – Jill $4, Jack $1. The game continues in this vein for a total of 99 rounds. If both players always choose to pass, they each receive a payoff of $50 at the end of the game. Note that the money is contributed by a third party and not by either player.

What does game theory predict? Using backward induction – which is the process of reasoning backward from the end of a problem – game theory predicts that Jack (or the first player) will choose to take on the very first move and both players will receive a $1 payoff.

In experimental studies, however, only a very small percentage of subjects chose to take on the very first move. This discrepancy can be explained by a couple of reasons. One reason is that some people are altruistic, and would prefer to cooperate with the other player by always passing, rather than taking down the pot. Another reason is that people may simply be incapable of making the deductive reasoning necessary to make the rational choice predicted by the Nash equilibrium. The fact that few people take the stash on the very first move is not too surprising, given the small size of the starting payoff when compared with the increasing payoffs as the game progresses.

  1. Backward Induction

    The process of deducing backwards from the end of a problem or ...
  2. Net Payoff

    The profit (or loss) from the sale of an item after the costs ...
  3. Nash Equilibrium

    A concept of game theory where the optimal outcome of a game ...
  4. Matching Pennies

    A basic game theory example that demonstrates how rational decision-makers ...
  5. Gaming Industry ETF

    Gaming ETFs invest in companies that generate revenue from the ...
  6. Discounted Payoff

    The discounted payoff is the repayment of a loan in an amount ...
Related Articles
  1. Insights

    The Basics Of Game Theory

    Here we take an introductory look at game theory and the terms involved, and introduce you to a simple method of solving games, called backwards induction.
  2. Investing

    Game Theory: Beyond the Basics

    Take your game theory knowledge to the next level by learning about the Nash Equilibrium.
  3. Tech

    You Love Video Games, But Do You Know How The Industry Works?

    Traditionally, the video game industry was limited to consoles, such as Microsoft’s (MSFT) Xbox and Sony’s (SNE) PlayStation, but it now includes PC games, mobile games and, in the near future, ...
  4. Tech

    Are Big Budget Video Games Dead?

    More people seem to be gaming on tablets and smartphones over consoles, which means this could be the end of big budget console games.
  5. Insights

    The 6 Most Famous Failed Video Game Makers (KING, ZNGA)

    The video-game industry pulls in $100 billion in revenue annually. Failed companies offer a cautionary tale.
  6. Tech

    Microsoft to Enable Game Gifting in the Xbox One Store

    Microsoft revealed in a tweet that it will soon let customers gift games via the Xbox One Store.
  7. Investing

    Shopify Launches Ecommerce Channel for Gaming Companies, Integrates with Apple

    Companies are set to benefit further from a new in-store sales channel for branded products.
  8. Tech

    Global Video Game Sales to Reach $91B in 2016

    New research from SuperData shows global interactive entertainment revenue up for the year.
  9. Insights

    Investors May Love the Fast Action in Video Games

    Video game companies that were once whipsawed by the "ship it and forget it" game cycle, are now thriving as they sell their games digitally.
  10. Investing

    Tencent Infects U.S. With Addictive Mobile Game

    Chinese internet company Tencent imports a highly addictive mobile game to the U.S. and Europe.
  1. How has the popularity of online gaming affected the internet sector?

    Discover how the increasingly popularity of online gaming has directly affected and fundamentally transformed the Internet ... Read Answer >>
  2. What is the difference between a dominant strategy solution and a Nash equilibrium ...

    Dive into game theory and the Nash equilibrium, and learn why the Nash equilibrium assumptions about information are less ... Read Answer >>
  3. What Happens When Borrowed Short Shares Are Sold?

    In a short-sale transaction, shares are borrowed from the lender and sold in the market. Read Answer >>
Hot Definitions
  1. Standard Deviation

    A measure of the dispersion of a set of data from its mean, calculated as the square root of the variance. The more spread ...
  2. Entrepreneur

    An entrepreneur is an individual who founds and runs a small business and assumes all the risk and reward of the venture.
  3. Money Market

    The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
  4. Perfect Competition

    Pure or perfect competition is a theoretical market structure in which a number of criteria such as perfect information and ...
  5. Compound Interest

    Compound Interest is interest calculated on the initial principal and also on the accumulated interest of previous periods ...
  6. Income Statement

    A financial statement that measures a company's financial performance over a specific accounting period. Financial performance ...
Trading Center