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We introduce the idea of a dining club to the Kolkata Paise RestaurantProblem. In this problem, $N$ agents choose (randomly) among $N$ restaurants,but if multiple agents choose the same restaurant, only one will eat. Agents inthe dining club will coordinate their restaurant choice to avoid choicecollision and increase their probability of eating. We model the problem ofdeciding whether to join the dining club as an evolutionary game and show thatthe strategy of joining the dining club is evolutionarily stable. We thenintroduce 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 eatbecause of collision with a non-dining club member. When non-dining clubmembers are allowed to cheat and share communal food within the dining club, weshow that a new unstable fixed point emerges in the dynamics. A bifurcationanalysis is performed in this case. To conclude our theoretical study, we thenintroduce evolutionary dynamics for the cheater population and study thesedynamics. Numerical experiments illustrate the behaviour of the system withmore than one dining club and show several potential areas for future research.

Stability of Dining Clubs in the Kolkata Paise Problem with and without Cheating