Fig. 5: Selection favors undemanding philanthropists over demanding philanthropists when the benefit-to-cost ratio exceeds a critical value.

Presented is the fixation probability of an individual using behavioral motivation A, i.e., (α_A, λ_A), in the population of individuals using behavioral motivation B, i.e., (α_B, λ_B), as a function of benefit b in the two-action donation game, with cost c = 1. We consider random regular networks (a) and BA scale-free networks (b). Selection favors behavioral motivation A over B if fixation probability ρ_A exceeds the horizontal line, i.e., ρ_A > 1/N. Squares indicate fixation probabilities by Monte Carlo simulations, and solid lines are analytical results. Red lines and squares represent the fixation probability of philanthropic motivation A, i.e., (1,0.01), in a population of B, i.e., (3,0.01), which shows that selection favors undemanding over demanding individuals as long as the benefit-to-cost ratio exceeds the critical ratio, i.e., b/c > (b/c)^*. Nonetheless, for motivations with α_A = α_B, the evolution of the motivation intensity is non-monotonous with benefit b --- both the small and large b/c favor a strong motivation, while the intermediate b/c favors weak motivation, as blue lines and dots show (the evolution of (2,0.03) in a population of (2,0.01)). The fixation probability of beneficial motivation A, ρ_A, is determined by the fractions of simulations where the beneficial motivation A reached fixation out of 2 × 10⁷ generations. Parameter values: population size N = 100 and average degree d = 6.