El Farol Bar problem

The El Farol bar problem is a problem in game theory. The problem is 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 preferences of the population can be described as follows: The El Farol bar problem is a problem in game theory. The problem is 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 preferences of the population can be described as follows: 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 pure strategy 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 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 that is a function of the number of players, the threshold for crowdedness, and the relative utility of going to a crowded or an uncrowded bar compared to staying home. There are also multiple Nash equilibria where one or more players use a pure strategy, but these equilibria are not symmetric. Several variants are considered in Game Theory Evolving by Herbert Gintis.