# El Farol Bar problem

Source: https://en.wikipedia.org/wiki/El_Farol_Bar_problem
Kiwi News: https://news.kiwistand.com/stories/El-Farol-Bar-problem?index=0x655939005e61bd1ce1aa99de6e067d858c69b22332d1bdc905d4f132a7d4d7913cd3468f
Submitted by macbudkowski.eth on 2023-11-18 UTC, 2 upvotes, 0 comments

## Summary

The El Farol Bar problem is a game theory problem in which a fixed population decides each Thursday whether to go to a bar that is fun only when less than 60% of the population attends. Everyone must decide at once without knowing others' choices, and the article says a deterministic symmetric strategy is guaranteed to fail, since a predicted empty bar fills up and a predicted crowded bar empties. It says a probabilistic mixed strategy does better and that the single-stage problem has a unique symmetric Nash equilibrium mixed strategy. The problem is named after a bar in Santa Fe, New Mexico, and was created in 1994 by W. Brian Arthur, though B. A. Huberman and T. Hogg formulated and solved it under another name six years earlier.

## Article

From Wikipedia, the free encyclopedia

The El Farol bar problem is a problem in game theory. Every Thursday night, a fixed population want to go have fun at the El Farol Bar, unless it's too crowded.

If less than 60% of the population go to the bar, they'll all have more fun than if they stayed home.

If more than 60% of the population go to the bar, they'll all have less fun than if they stayed home.

Everyone must decide at the same time whether to go or not, with no knowledge of others' choices.

If everyone uses a deterministic pure strategy which is symmetric (same strategy for all players), it is guaranteed to fail no matter what it is. If the strategy suggests it will not be crowded, everyone will go, and thus it will be crowded; but if the strategy suggests it will be crowded, nobody will go, and thus it will not be crowded, but again no one will have fun. Better success is possible with a probabilistic mixed strategy. For the single-stage El Farol Bar problem, there exists a unique symmetric Nash equilibrium mixed strategy where all players choose to go to the bar with a certain probability, determined according to the number of players, the threshold for crowdedness, and the relative utility of going to a crowded or uncrowded bar compared to staying home. There are also multiple Nash equilibria in which one or more players use a pure strategy, but these equilibria are not symmetric.[1] Several variants are considered in Game Theory Evolving by Herbert Gintis.[2]

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

Named after a bar in Santa Fe, New Mexico, the problem was created in 1994 by W. Brian Arthur. However, under another name, the problem was formulated and solved dynamically six years earlier by B. A. Huberman and T. Hogg.[3] See Kolkata Paise Restaurant Problem for extending it from binary choice (go to the bar or stay home) to multiple options for each player.

↑ Whitehead, Duncan (2008-09-17). "The El Farol Bar Problem Revisited: Reinforcement Learning in a Potential Game" (PDF). University of Edinburgh School of Economics. Retrieved 2014-12-13.

↑ Gintis, Herbert (2009). Game Theory Evolving. Vol. 6. Princeton University Press. p. 134. ISBN 978-0-691-14051-3.

↑ "The Ecology of Computation", Studies in Computer Science and Artificial Intelligence, North Holland publisher, page 99. 1988.

Arthur, W. Brian (1994). "Inductive Reasoning and Bounded Rationality" (PDF). American Economic Review: Papers and Proceedings. 84: 406–411. Archived from the original (PDF) on 2015-02-20. Retrieved 2014-12-13.

Minority Games (a popularization account)