The rise and fall of donation behavior through reputation

Unlike in the standard public goods game (PGG), real-life donors (e.g. to charities) rarely receive any direct benefits from their donation behaviors to a disaster area, but donations are always prevalent. This paper studies why donation behaviors are common and the factors that can influence their propagation. The interactions among individuals are divided into two phases, including all individuals independently making decisions about whether to donate (namely donation game) and playing prisoner's dilemma with their neighbors in a structured population. We first explore the evolution of donation behaviors in the aforementioned spatial games with four competing strategies. As expected, “extreme altruists” can hardly survive in the population with “extreme egoists” unless they become “shunners”, who decide whether to cooperate in the prisoner's dilemma on the basis of the reputation of their opponents. Given the complexity of the real world, we further study the evolution of a more complex six-strategy population with additional two peculiar strategies, “hypocrites” and “realists”. We have observed more complicated phase diagrams, and multiple discontinuous phase transitions as well as a variety of spontaneously formed three-strategy cyclic states. Through the analysis of the phases and spatial dynamics, we find that these two introduced strategies will have an adverse impact on the popularization of donation behaviors in their own ways under different circumstances.