# El Farol Minority Game

Interactive simulation of bounded rationality and inductive reasoning — the El Farol Bar Problem by W. Brian Arthur (1994)

> Canonical page: https://elysiatools.com/en/visualizations/el-farol-game

- **Category:** Math

## Overview

Interactive simulation of W. Brian Arthur's 1994 El Farol Bar Problem demonstrating bounded rationality, inductive reasoning, and emergent self-organization. N agents independently decide each week whether to attend a bar with capacity threshold θ. Each agent maintains S prediction strategies (linear combinations of past m attendance values plus heuristics: mirror, mean, cycle, contrarian, last-value) and follows the one with lowest cumulative squared prediction error. Decision noise ε models irrational whims. Features three synchronized visualizations: (1) Attendance time series showing convergence to θ with green/red dots for below/above threshold, mean line, and threshold dashed line; (2) Prediction RMSE over time showing how aggregate forecasting accuracy evolves; (3) Strategy distribution histogram showing active linear vs heuristic strategies. Adjustable parameters: N=10-500 agents, θ=10-95 threshold, m=2-12 memory length, S=2-12 strategies per agent, ε=0-0.3 decision noise, weeks to run. Three simulation modes: run all at once, single-step for pedagogical inspection, or animated auto-run. Statistics panel tracks week, attendance, running mean, standard deviation, happy rate (% weeks below θ), and optimality rate (closeness of mean to θ). Education covers Arthur's original formulation, the impossibility of rational expectations, inductive reasoning as realistic bounded rationality, strategy ecology and perpetual disequilibrium, negative feedback convergence mechanism, and applications in financial markets (technical analysis as prediction rules, Minority Game econophysics), traffic routing (GPS creates real-time El Farol), prediction markets (diversity of models beats individual accuracy), and network resource allocation (distributed load balancing). 8 languages (zh, en, es, fr, de, ru, pt, ja).

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