# El Farol Bar Model

The El Farol bar model describes chaotic behavior of bar attendees, where the number of people attending the bar fluctuates around a certain threshold. It was created in 1994 by W. Brian Arthur, an economics who helped start the Santa Fe Institute. In its more general form it is known as the minority game, where people try to be in the minority for a certain choice, because in the end minority side wins. The El Farol bar model is named after a bar in Santa Fe, New Mexico. Once a week the bar had live Irish music that was enjoyable only if the place wasn't too crowded. The problem was to decide when to go and when to stay home.

The problem is modelled as follows: There is a particular, finite population of people. Every Thursday night, all of these people want to go to the El Farol Bar. However, the El Farol is quite small, and it's no fun to go there if it's too crowded. So much so, in fact, that the following rules are in place:

• If less than 60% of the population go to the bar, they'll all have a better time than if they stayed at home.
• If more than 60% of the population go to the bar, they'll all have a worse time than if they stayed at home.

Unfortunately, it is necessary for everyone to decide at the same time whether they will go to the bar or not. They cannot wait and see how many others go on a particular Thursday before deciding to go themselves on that Thursday.

One aspect of the problem is that, no matter what method each person uses to decide if they will go to the bar or not, if everyone uses the same method it is guaranteed to fail. If everyone uses the same deterministic method, then if that method suggests that the bar will not be crowded, everyone will go, and thus it will be crowded; likewise, if that method suggests that the bar will be crowded, nobody will go, and thus it will not be crowded. Often the solution to such problems in game theory is to permit each player to use a mixed strategy, where a choice is made with a particular probability. In the case of the El Farol Bar problem, however, no mixed strategy exists that all players may use in equilibrium.

In some variants of the problem, the people are allowed to communicate with each other before deciding to go to the bar. However, they are not required to tell the truth.

One variant of the El Farol Bar problem is the minority game proposed by Yi-Cheng Zhang and Damien Challet. In the minority game, an odd number of players each must choose one of two choices independently at each turn. The players who end up on the minority side win. While the El Farol Bar problem was originally formulated to analyze a decision-making method other than deductive rationality, the minority game examines the characteristic of the game that no single strategy of any kind may be adopted by all participants in equilibrium.