Kolkata Paise Restaurant Problem

Abstract

The Kolkata Paise Restaurant (KPR) problem is repeatedly played among a large number N of agents or players having no interaction amongst themselves. The agents or players choose from $N'$ restaurants each evening independently ($N '\le N$). In the problem the prospective customers or players each have the same set of data regarding the success or failure of the various restaurants: the data set gives the number of prospective customers arriving at each restaurant for the past evenings. Let us assume that the price for the meal to be the same for all the restaurants though the customers can have a ranking of preference for each restaurant (agreed upon by all customers). For simplicity we also assume that each restaurant can serve only one customer any evening. As already mentioned, information about the customer distributions for earlier evenings is available to everyone. Each customer will try to go to the restaurant with the highest possible rank while avoiding the crowd so as to be able to get dinner there. If any restaurant is chosen by more than one customer on any evening, one of them will be randomly chosen (each of them is anonymously treated) and will be served. The rest will not get dinner that evening. The customers collectively learn from their attempts in the past, how to avoid the crowd to get the meal from a high ranking restaurant.