The Kolkata Paise Restaurant Problem and Resource Utilization

TL;DR

This paper analyzes the Kolkata Paise Restaurant problem, exploring its dynamics, strategies, and resource utilization in large populations, highlighting issues of under-utilization and potential improvements.

Contribution

It introduces one-shot KPR games and studies the long-term dynamics and resource utilization in the repeated game setting for large N.

Findings

Under-utilization of resources in many strategies

Myopic strategies lead to lower aggregate payoff

Analysis of steady state behavior in large N limit

Abstract

We study the dynamics of the "Kolkata Paise Restaurant problem". The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.