Kolkata Paise Restaurant Problem in Some Uniform Learning Strategy Limits

TL;DR

This paper analyzes the dynamics of uniform probabilistic learning strategies in the Kolkata Paise Restaurant problem, focusing on how agents learn and adapt to optimize restaurant utilization in a multi-agent setting.

Contribution

It introduces a probabilistic learning framework for the Kolkata Paise Restaurant problem and analytically examines restaurant utilization in limiting cases.

Findings

Analytical insights into restaurant utilization limits

Effectiveness of uniform probabilistic strategies

Behavior of agents in multi-agent learning scenarios

Abstract

We study the dynamics of some uniform learning strategy limits or a probabilistic version of the "Kolkata Paise Restaurant" problem, where N agents choose among N equally priced but differently ranked restaurants every evening such that each agent can get dinner in the best possible ranked restaurant (each serving only one customer and the rest arriving there going without dinner that evening). We consider the learning to be uniform among the agents and assume that each follow the same probabilistic strategy dependent on the information of the past successes in the game. The numerical results for utilization of the restaurants in some limiting cases are analytically examined.