TheEl Farol bar problem is a problem ingame theory. Every Thursday night, a fixed population want to go have fun at the El Farol Bar, unless it's too crowded.
Everyone must decideat the same time whether to go or not, with no knowledge of others' choices.
Paradoxically, if everyone uses a deterministicpure 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 itwill be crowded; but if the strategy suggests it will be crowded, nobody will go, and thus it willnot be crowded, but again no one will have fun. Better success is possible with a probabilisticmixed strategy. For the single-stage El Farol Bar problem, there exists a unique symmetricNash 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 inGame Theory Evolving byHerbert 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 inSanta Fe, New Mexico, the problem was created in 1994 byW. Brian Arthur. However, under another name, the problem was formulated and solved dynamically six years earlier by B. A. Huberman and T. Hogg.[3] SeeKolkata Paise Restaurant Problem for extending it from binary choice (go to the bar or stay home) to multiple options for each player.
