# Guess 2/3 of the average

Guess 2/3 of the average

In game theory, Guess 2/3 of the average is a game where several people guess what 2/3 of the average of their guesses will be, and where the numbers are restricted to the real numbers between 0 and 100. The winner is the one closest to the 2/3 average.

Equilibrium analysis

In this game there is no strictly dominant strategy. However, there is a unique pure strategy Nash equilibrium. This equilibrium can be found by iterated elimination of strictly dominated strategies. Guessing any number that lies above 66.67 is dominated for every player since it cannot possibly be 2/3rds of the average of any guess. These can be eliminated. Once these strategies are eliminated for every player, any guess above 44.45 is strictly dominated for every player since no player will guess above 66.67 and 2/3 of 66.67 is approximately 44.45. This process will continue until all numbers above 0 have been eliminated.

This degeneration does not occur in quite the same way if choices are restricted to, for example, the integers between 0 and 100. In this case, all integers except 0 and 1 vanish; it becomes advantageous to select 0 if one expects that at least 1/4 of all players will do so, and 1 if otherwise. (In this way, it is a lopsided version of the so-called "consensus game", where one wins by being in the majority.)

Experimental results

This game is a common demonstration in game theory classes, where even economics graduate students fail to guess 0. When performed among ordinary people it is usually found that the winner guess is much higher than 0, e.g., 21.6 was the winning value in a large internet-based competition organized by the Danish newspaper Politiken. This included 19,196 people and with a prize of 5000 Danish kroner. dk icon Astrid Schou, [http://politiken.dk/erhverv/article123939.ece Gæt-et-tal konkurrence afslører at vi er irrationelle] , Politiken; includes a [http://konkurrence.econ.ku.dk/distribution?id=1237&d=6655488e6252d35e705500b68a339c50 histogram] of the guesses. Note that some of the players guessed close to 100.]

The Museum of Money has an [http://www.museumofmoney.org/exhibitions/games/guessnumber.htm interactive flash applet of the game] , where each given answer will be used to calculate the current outcome.

Rationality versus common knowledge of rationality

This game illustrates the difference between perfect rationality of an actor and the common knowledge of rationality of all players. Even a perfectly rational player playing in such a game should not guess 0 unless they know that the other players are rational as well and that all players' rationality is common knowledge. If a rational player reasonably believes that other players will not follow the chain of elimination described above, it would be rational for them to guess a number above 0.

Interestingly, we can suppose that all the players are rational, but they do not have common knowledge of each other's rationality. Even in this case, it is not required that every player guess 0, since they may expect each other to behave irrationally.

Notes

* Keynesian beauty contest

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• The Market for Lemons — The Market for Lemons: Quality Uncertainty and the Market Mechanism is a 1970 paper by the economist George Akerlof. It discusses information asymmetry, which occurs when the seller knows more about a product than the buyer. A lemon is an… …   Wikipedia

• The Catholic Guy — is a radio talk show currently aired on The Catholic Channel on Sirius Satellite Radio. The Catholic Guy has been on the air since December 4, 2006. It is hosted by Emmy Award winning Lino Rulli. The Catholic Guy show discusses life, religion,… …   Wikipedia

• The Wisdom of Crowds — The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations , first published in 2004, is a book written by James Surowiecki about the aggregation of information in… …   Wikipedia

• The New Palgrave Dictionary of Economics — (2008), 2nd Edition, is an eight volume reference work, edited by Steven N. Durlauf and Lawrence E. Blume. It contains 5.8 million words and spans 7,680 pages with 1,872 articles. Included are 1057 new articles and, from earlier, 80 essays that… …   Wikipedia

• The Chris Moyles Show — This article is about The Chris Moyles Show. For him as an individual, see Chris Moyles. The Chris Moyles Show Genre Comedy, talk Running time 210 minutes (6:30 10:00 am) …   Wikipedia

• The Biggest Loser: Couples 2 — For the Australian series, see The Biggest Loser Australia: Couples 2. The Biggest Loser: Couples 2 Format Reality TV Created by Dave Broome Presented by Alison Sweeney Starring Bob Harper …   Wikipedia

• The Joker's Wild — infobox television show name = The Joker s Wild caption = Show logo, 1972 1975 format = Game show rating = TV G runtime = 30 minutes with commercials creator = Jack Barry starring = Jack Barry (host, 1972 84) Bill Cullen (host, 1984 86) Jim Peck… …   Wikipedia

• The Castle of Llyr — infobox Book | name = The Castle of Llyr title orig = translator = image caption = Recent US paperback cover author = Lloyd Alexander cover artist = Evaline Ness country = United States language = English series = The Chronicles of Prydain genre …   Wikipedia

• The Book of Dreams — Infobox Book name = The Book of Dreams title orig = translator = image caption = first edition cover of the The Book of Dreams author = Jack Vance illustrator = cover artist = Ken W. Kelly country = United States language = English series = Demon …   Wikipedia

• The Mad Monster — Infobox Film name = The Mad Monster caption = A promotional film poster for The Mad Monster. director = Sam Newfield producer = Sigmund Neufeld writer = Fred Myton starring = Johnny Downs George Zucco Anne Nagel Reginald Barlow music = David… …   Wikipedia