Kolkata Restaurant Problem as a generalised El Farol Bar Problem

TL;DR

This paper generalizes the El Farol bar problem to multiple restaurants, analyzing the resulting Kolkata restaurant problem, revealing that fluctuations follow an inverse cubic law similar to stock market behavior.

Contribution

It introduces a generalized model of the El Farol problem for multiple restaurants and provides exact analysis in certain limits, connecting fluctuation behavior to stock market phenomena.

Findings

Fluctuations in restaurant service follow an inverse cubic law.

The model can be exactly analyzed in specific limiting cases.

The behavior parallels stock market fluctuation patterns.

Abstract

Generalisation of the El Farol bar problem to that of many bars here leads to the Kolkata restaurant problem, where the decision to go to any restaurant or not is much simpler (depending on the previous experience of course, as in the El Farol bar problem). This generalised problem can be exactly analysed in some limiting cases discussed here. The fluctuation in the restaurant service can be shown to have precisely an inverse cubic behavior, as widely seen in the stock market fluctuations.