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.

与标准的公共物品游戏 (PGG) 不同，现实生活中的捐赠者（例如慈善机构）很少从他们向灾区的捐赠行为中获得任何直接利益，但捐赠总是很普遍。本文研究了捐赠行为为何如此普遍以及影响其传播的因素。个体之间的互动分为两个阶段，包括所有个体独立做出是否捐赠的决定（即捐赠博弈）和在结构化种群中与邻居玩囚徒困境。我们首先用四种竞争策略探索上述空间博弈中捐赠行为的演变。正如预期的那样，“极端利他主义者”很难在“极端利他主义者”的人群中生存，除非他们成为“回避者”，他们根据对手的声誉决定是否在囚徒困境中合作。鉴于现实世界的复杂性，我们进一步研究了一个更复杂的六策略群体的演变，以及另外两个特殊的策略，“伪君子”和“现实主义者”。我们观察到了更复杂的相图、多个不连续的相变以及各种自发形成的三策略循环状态。通过对阶段和空间动态的分析，我们发现这两种引入策略在不同情况下会以各自的方式对捐赠行为的普及产生不利影响。我们进一步研究了一个更复杂的六策略群体的演变，还有另外两个特殊的策略，“伪君子”和“现实主义者”。我们观察到了更复杂的相图、多个不连续的相变以及各种自发形成的三策略循环状态。通过对阶段和空间动态的分析，我们发现这两种引入策略在不同情况下会以各自的方式对捐赠行为的普及产生不利影响。我们进一步研究了一个更复杂的六策略群体的演变，还有另外两个特殊的策略，“伪君子”和“现实主义者”。我们观察到了更复杂的相图、多个不连续的相变以及各种自发形成的三策略循环状态。通过对阶段和空间动态的分析，我们发现这两种引入策略在不同情况下会以各自的方式对捐赠行为的普及产生不利影响。