  We introduce the idea of a dining club to the Kolkata Paise Restaurant
Problem. In this problem, $N$ agents choose (randomly) among $N$ restaurants,
but if multiple agents choose the same restaurant, only one will eat. Agents in
the dining club will coordinate their restaurant choice to avoid choice
collision and increase their probability of eating. We model the problem of
deciding whether to join the dining club as an evolutionary game and show that
the strategy of joining the dining club is evolutionarily stable. We then
introduce an optimized member tax to those individuals in the dining club,
which is used to provide a safety net for those group members who don't eat
because of collision with a non-dining club member. When non-dining club
members are allowed to cheat and share communal food within the dining club, we
show that a new unstable fixed point emerges in the dynamics. A bifurcation
analysis is performed in this case. To conclude our theoretical study, we then
introduce evolutionary dynamics for the cheater population and study these
dynamics. Numerical experiments illustrate the behaviour of the system with
more than one dining club and show several potential areas for future research.
