Evolution of generosity in the demand game
An ecological system often requires moderate, and sometimes even generous interactions among constituents for achieving a sustainable coexistence. Here we propose a configuration individual-based model for demonstrating the evolution of generosity in an evolutionary demand game. In the game, two players, proposers and responders, simultaneously make their demands. If the sum of demands is no more than the total amount of the available resource at each game, each player obtains its own demand. However, both players get nothing if the sum exceeds the total amount. We incorporated generosity by discounting players demands. In every generation, random pairs were formed, and each pair played the demand game. For the next generation, individuals left a number of offspring proportional to their total payoff. Demand and generosity levels of an individual were inherited by its offspring with slight modification by a small random mutation. When only proposers were allowed to discount their demands, distribution of generosity levels had its mode at zero, and hence generosity did not evolve. However, when both proposers and receivers were allowed to discount their demands, the mean generosity level rose from zero. The resultant populations were not homogeneous, but were made of heterogeneous individuals with high and low generosity levels. Mean demand and generosity levels fluctuated greatly because of the neutral selection for the demand and generosity combinations that equally maximized the payoff of the demand game. Spatially limited interaction increased generosity levels even if only proposers discounted their demands.