El Farol Bar problem

Named after a bar in Santa Fe, New Mexico, the problem was created in 1994 by W. Brian Arthur.

[3] A variant is the Minority Game proposed by Yi-Cheng Zhang and Damien Challet from the University of Fribourg.

As in the El Farol Bar problem, no single (symmetric) deterministic strategy can give an equilibrium, but for mixed strategies, there is a unique symmetric Nash equilibrium (each player chooses with 50% probability), as well as multiple asymmetric equilibria.

[11] Strategies are evaluated based on their aggregate payoff and/or the proportion of attended restaurants (utilization ratio).

This is a better result than deterministic algorithms or simple random choice (noise trader), with utilization fraction 1 - 1/e ≈ 0.63.

[12] Increased utilization for customers having allowance for local optimization search using Traveling Salesman Problem type algorithms have also been studied.