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The Kolkata Paise Hotel Problem

By Bikas K. Chakrabarti, Manipuspak Mitra and Anindya-sundar Chakrabarti

Abstract

Abstract: For N possible customers or agents and N pricewise identical restaurants (or any other type of service providers), we study the collective dynamical states of choices. Each evening the choice problem of any agent is to go to a restaurant. The agent makes this choice based on two things (a) his/her own past experiences and (b) the past restaurant utilisation records (available to everyone). Moreover, each agent makes his/her choice independent of others, that is we assume that there is no interaction across agents. If more than one agent turns up in any particular restaurant, one of them is randomly selected by the restaurant and the rest do not get any dinner that evening. Although the prices are the same for all the restaurants, there is a prevailing opinion across agents about the preference rankings of these restaurants and it is commonly shared by all the N agents. Of the N N possible states, only N! states are “socially efficient ” or Pareto efficient in the sense that no agent can be made better off without making any other agent worse off. This is achieved when all the agents get their dinners. In the absence of mutual interaction across agents occurance of such a Pareto efficient state has a very low probability. However, given the common preferenc

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