Statistics of the Kolkata Paise Restaurant Problem

TL;DR

This paper analyzes stochastic learning strategies in the Kolkata Paise Restaurant problem, revealing that simple strategies can outperform more complex ones in resource utilization, with some strategies achieving up to 80% efficiency.

Contribution

It introduces and compares various stochastic learning strategies for the problem, showing that naive approaches can outperform smarter strategies in resource utilization.

Findings

Naive strategies can outperform smarter ones in utilization.

A stochastic strategy achieves up to 80% service utilization.

Analytical examination of limiting cases supports numerical results.

Abstract

We study the dynamics of a few stochastic learning strategies for the 'Kolkata Paise Restaurant' problem, where N agents choose among N equally priced but differently ranked restaurants every evening such that each agent tries get to dinner in the best restaurant (each serving only one customer and the rest arriving there going without dinner that evening). We consider the learning strategies to be similar for all the agents and assume that each follow the same probabilistic or stochastic strategy dependent on the information of the past successes in the game. We show that some 'naive' strategies lead to much better utilization of the services than some relatively 'smarter' strategies. We also show that the service utilization fraction as high as 0.80 can result for a stochastic strategy, where each agent sticks to his past choice (independent of success achieved or not; with probability decreasing inversely in the past crowd size). The numerical results for utilization fraction of the services in some limiting cases are analytically examined.