Talk:El Farol Bar problem

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[edit] Prisoner's Dilemma?

Thanks for adding this entry, I think its a really cool problem and I'm glad its here. I'm also happy to have folks working on the game theory section, we are an elite few :) I removed two references comparing this problem to the prisoner's dilemma. I'm not sure I see the similarity between the two games. In the el farol problem, the nash equilibrium is the most socially efficient among all strategy choices, right? That is society as a whole will not do (strictly) better if a non-nash equilibrium set of strategies is chosen. The interesting thing in the prisoner's dilemma is that self-interest leads to socially inefficient strategy choices, which doesn't seem to be a problem here. You might say that the mixed strategy equilibrium is inefficient, but this is true for many games (like for instance battle of the sexes) which I think are more similar to the el farol problem. I may be misunderstanding the relationship, but it seems more misleading than helpful. Please add it back in if I'm wrong, but it would be good to say more about the relationship. best, --Kzollman 06:23, Jun 26, 2005 (UTC)

This article needs a quote from Yogi Berra.

[edit] Emphasis on repeated plays

It seems that there should be more emphasis that this game is a repeated game. That is, participants do not simply play once on one Thursday afternoon; it is critical to the character of the game that it is infinitely repeated and that the attendence of previous Thursdays is available to the same participants.

Also, it seems that the El Farol bar problem is not a specific case of the "more general" Minority Game; there are at least three fundamental differences. In the minority game, only an odd number of people can play (whereas any number of people may be participate in El Farol). Also, there are three outcomes possible in the El Farol bar (positive utility from attending the bar, negative utility from attending the bar, and zero utility from staying home) whereas there are only two outcomes possible in the minority game (positive utility from being in the minority and negative utility from being in the majority). Finally, the minority is the not the group that gains utility in the El Farol bar; if 59% attend the bar, then the majority will gain utility. Basically, I believe the character of the El Farol bar problem is substantively different than that of the Minority Game, even if both games demonstrate the same impossible-to-devise-a-superior-strategy characteristic. --Bjp716 02:08, Nov 7, 2006 (UTC)

Thank you for your suggestion. It sounds like you know more about this game than I do. I'd like to invite you to make any changes you see fit to the article, I suspect they will be most welcome. If other editors have concerns with your changes, they will discuss them here. Thanks again and welcome to wikipedia. --best, kevin [kzollman][talk] 02:22, 8 November 2006 (UTC)

[edit] Mixed Strategy Solution

I agree that the important aspect of the game is iteration and there are no solutions based on analysis of past attendance. However there is a solution based on a 'mixed strategy' although it is a decision theoretic problem not a game - if each player decides to attend 50% of days say by flipping a coin then for sufficiently large populations the bar will virtually never be crowded. If each player has access to a random number generator then they can evolve an optimal strategy using the following algorithm:

1. Choose a threshold 0 > t < 1 at random
2. Generate a random number n
3. If n > t

     go to the bar
     If bar crowded 
          increase t
     Endif
  Else 
     stay at home
     If bar not crowded 
         decrease t
     Endif
  Endif

4. Go to 2

You could use bayes' formula to adjust t but any incremental change will work.

This is easy to model on a spreadsheet. It is also possible to introduce elements of heterogeneity amongst players such as risk aversion and crowd tolerance.

The Bar problem is a useful teaching tool because it emphasizes the importance of analysis a problem to determining the right data to support the decision and the danger of collecting data just because it is available and easy to do so.-- 62.31.119.101 (talk) 17:41, 22 January 2008 (UTC)

[edit] Equilibrium

In the case of the El Farol Bar problem, however, no mixed strategy exists that all players may use in equilibrium.

Why is going with 60% probability not an equilibrium? Even Brian's article seems to say it is. --Tgr (talk) 19:03, 22 January 2008 (UTC)

If each member of the population attended 60% of the time then the average attendance would be 0.6P (where P is the size of the population) which means that the bar would be crowded 50% of the time. Assuming the negative utility of a crowded bar is equal to the positive utility of an uncrowded bar then going 60% of the time would yield zero utility. Everybody would be better off if everybody went somewhat less than 60% of the time. --NigelPhil (talk) 11:20, 25 January 2008 (UTC)NigelPhil