Evolutionary Stability of Multiple Dining Clubs in the Kolkata Paise Problem with Freeloaders

We study the Kolkata Paise problem with dining clubs. Here, $N$ agents choose (randomly) among $N$ restaurants, but if multiple agents choose the same restaurant, only one will eat. Agents in a dining club coordinate their restaurant choices to avoid collision and increase their probability of eating. Using an evolutionary game, we show that the strategy of joining the dining club is evolutionarily stable. We introduce a taxation system to enable resource sharing and show that there is an optimal tax that preserves evolutionary stability of the dining club. We then show that when multiple dining clubs are available, the system tends to a monoculture. 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 and bifurcation analysis shows that the mono-culture of a single dining club remains stable, but not globally attracting. Future work is also considered.