Kolkata Paise Restaurant Problem and the Cyclically Fair Norm

In this paper we revisit the Kolkata Paise Restaurant problem by allowing for a more general (but common) preference of the n customers defined over the set of n restaurants. This generalization allows for the possibility that each pure strategy Nash equilibrium differs from the Pareto efficient allocation. By assuming that n is small and by allowing for mutual interaction across all customers we design strategies to sustain cyclically fair norm as a sub-game perfect equilibrium of the Kolkata Paise Restaurant problem. We have a cyclically fair norm if n strategically different Pareto efficient strategies are sequentially sustained in a way such that each customer gets serviced in all the n restaurants exactly once between periods 1 and n and then again the same process is repeated between periods (n+1) and 2n and so on.