Talk:Guess 2/3 of the average

Level 0 is 50
In a {0, 1, ..., 100} Level-0 is not defined as 67, as in the article, but 50, as Level-0 in the K-level literature means a completely naive agent, whose choice is an uniform random draw over the support. 67 would be Level-1, if we follow the convention. Please see the cited article, for example. — Preceding unsigned comment added by 130.232.38.92 (talk) 09:55, 14 February 2023 (UTC)


 * I agree. It should be changed 31.161.145.185 (talk) 16:36, 6 April 2023 (UTC)

Poor article introduction
This is purely an article structure note and not about the actual content or the game, but the introduction here is lacking. For starters, the actual game isn't defined, which might seems like it's implied in the title, but it seems careless to jump straight into the crowd theory without even mentioning that the game depends works on answers from multiple people. 125.253.100.84 (talk) 18:05, 25 March 2013 (UTC)

All strictly dominated by 0?
Why is 1 dominated by 0? If more than 3/4 of players guess 1 and the rest 0 then 1 seems to win.--Henrygb 03:02, 17 December 2005 (UTC)
 * Thanks for pointing this out, this might not be clear from the article. 1 is not strictly dominated by 0.  1 is strictly dominated by 2/3 since if everyone guesses 1, 2/3 of 1 is 2/3.  Then if everyone guesses 2/3, 2/3 is strictly dominated by 4/9, etc.  --best, kevin [kzollman][talk] 23:14, 17 December 2005 (UTC)
 * If you change the article to real numbers then you have to change "66". Also, if "between 0 and 100" means "strictly between" then 0 is not a permitted choice. --Henrygb 00:56, 19 December 2005 (UTC)

"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 she knows that the other players are rational as well."
 * Isn't it true that even this condition is too weak? In fact, a perfectly rational player should guess 0 if and only if he knows that all other players know that all other players know that all other players know ...(to infinity)...that all other players are rational? Isn't this a difficult condition to satisfy? -- posted by JRC 1/17/06


 * What you're describing is common knowledge of rationality. Indeed it is a very difficult condition to satisfy, which is exactly the point of this game.  In other games, nash equilibrium play is the best response even when common knowledge is not satisfied.   So, this game isn't necessarily a demonstration that nash equilibrium play is not the best response in all cases.  But it does show the strength of the assumptions. --best, kevin [kzollman][talk] 19:54, 26 January 2006 (UTC)


 * The desription of Nash's equilibrium is in fact only true when the number of players is three or more. The case of two players, both players must simply bid a number greater than the other to win, hence the equilibium point shifts to 100.203.20.192.54 05:12, 19 January 2007 (UTC)
 * While the game is normally played with more than two players, I don't understand your point. If I guess 25 and you guess 24, the average is 24.5.  (2/3)*24.5 = 16.33 which is closer to 24 than to 25.  So the lower guess wins.  Am I missing something? --best, kevin [kzollman][talk] 07:08, 19 January 2007 (UTC)

Most rational answer
Say, one assumes that the acceptance of a distribution of rationality is, in itself, rational. Wouldn't the most rational decision itself be located in 22.2 then, at first iteration? Only the most rational people would choose this answer, of course, and less rational choices made would be distributed towards 67 and 0. Iteration of this will move the result around a bit. But I guess the main problem of the assumption is that X% rational person would also choose a result that is X% of the optimal value. More likely is that an unrational person would choose a random value between 0 and 67, and the randomness of the value with respect to the optimal value of ~22 would decrease with increasing rationality. Then, this should be iterated until it converges (if it does converge) to the optimal answer, or a distribution of answers. -- Mipmip 10:57, 20 October 2006 (UTC)

The whole line of reasoning about 22 seems flawed to me. First it is assumed that there exists common knowledge of rationality, because it is stated that "perfect reasoning" leads to a choice of 0. But then, the very fact that the article is looking for some other optimal choice means that there is not common knowledge of rationality. Therefore, some of the "most rational" people may choose a value other than 0, and so a symmetric distribution of rationality does not necessarily imply a symmetric distribution of guesses. Then again, it could be that I'm missing something here. --Benna 08:24, 29 November 2006 (UTC)

Finally, a web poll might not be the optimal test for this, as people might purposely give the wrong answer. It might be more interesting if people would actually have to lay money in for this. Even then, if all people would choose 0, the chance of winning simply becomes 1/(number of contestants), which makes it like joining a lottery. To increase your winning chances, it would be better to buy several chances, do several lost bets that are near the max. value, and do a serious bet just above 0. -- Mipmip 10:57, 20 October 2006 (UTC)

Other experiments
James Montier conducted a practical experiment by emailing over 1000 economists. The winning result was also around 21. Some of his responses were interesting: "100 - I am irrational". He also concluded that the best approach was to assign a distribution percentage to each order of thinking. —Preceding unsigned comment added by 58.107.40.223 (talk) 12:43, 12 August 2010 (UTC)

Politiken link broken
Maybe not on the page anymore. I tried the link today but got redirected to the main page -- Mipmip 11:13, 20 October 2006 (UTC)
 * Fixed. —Preceding unsigned comment added by Cherkash (talk • contribs) 23:09, 3 August 2010 (UTC)

Rationality versus common knowledge of rationality
There is a flaw with this section's explanation. The least rational person should be starting with 33.33 as his bid (as 33.33 is 2/3 of 50, which in turn is an average expected value for symmetric distributions from 0 to 100). So the whole scaling is off by a factor of 2, and the person who is rational but expects others to be irrational should choose 11.11. -- cherkash 20:08, 4 December 2006 (UTC)


 * The least rational person would choose 100, I think. Certainly that choice is less rational than the one you suggest. :)  Either way, I have removed the section in question.  I am worried that it is original research.  If the original author would like it reinserted, she should provide a citation for the material.  --best, kevin [kzollman][talk] 00:51, 5 December 2006 (UTC)

References?
There is a blatant lack of references, beginning with John Maynard Keynes who coined the notion "beauty contest", under which this game is known in economics over the classic studies by Bosch-Domenech and others to the theoretical accounts for out-of-equilibrium play like noisy introspection, quantal response equilibrium and the cognitive hierarchy model. Right now if you look at the notes section, you get the impression that this game is a Danish invention.
 * They're not the same game, though they are closely related. I've added a see also to the Keynesian beauty contest, but it could do with being mentioned in the main body of the article. EdC (talk) 02:57, 30 January 2008 (UTC)

Defecting
If the bounds are large enough relative to the amount of people playing, you can rationally choose the largest number possible. This puts you closer to the 2/3 average but on the other side of it. Then if people expect you to play that strategy, they can start inching their numbers higher. The whole thing can oscillate depending on the initial parameters. The usual way to defeat this is by using Price Is Right rules: no going over.

No mention of Princess Bride?
Inconceivable!!! S Philbrick (Talk)  14:27, 26 April 2022 (UTC)