连续自愿公益博弈中的无约束策略多样化与崩溃
Unchecked strategy diversification and collapse in continuous voluntary public good games
摘要：
合作或背叛、参与或退出是自由社会中类似游戏的活动中众所周知的行为选择，但这些行为特征在个体层面上的共同进化动力学还没有得到很好的理解。在这里，我们研究了连续自愿的公共产品博弈，其中个人有两种类型的连续值选项：加入公共产品博弈的概率和合作投资的水平在游戏中。我们的数值计算结果揭示了迄今未报道的现象：（1）进化动力学最初的特点是在个人的合作和参与水平的振荡，在人口水平的振荡，以前已经报道。(ii)最终，人口的平均合作和参与水平收敛并稳定在一个中心。(iii)然后，一个最奇特的现象出现了：种群中存在的策略多样化，并产生了一个“云”，每个人都尝试不同的策略，只要种群的合作和参与水平保持平衡，这个过程就会继续下去。然而，随着时间的推移，不平衡作为随机漂移的结果而积累起来，战略多样性云会突然崩溃。然后，该过程以循环的方式再次重复。为了理解上述三种现象，我们研究系统分析使用自适应动态技术。我们的分析揭示了支持意外和令人惊讶的进化动力学的机制。
英文摘要：
Cooperation or defection and participation or withdrawal are well-known options of behavior in game-like activities in free societies, yet the co-evolutionary dynamics of these behavioral traits in the individual level are not well understood. Here we investigate the continuous voluntary public good game, in which individuals have two types of continuous-valued options: a probability of joining the public good game and a level of cooperative investment in the game. Our numerical results reveal hitherto unreported phenomena: (i) The evolutionary dynamics are initially characterized by oscillations in individual cooperation and participation levels, in contrast to the population-level oscillations that have previously been reported. (ii) Eventually, the population's average cooperation and participation levels converge to and stabilize at a center. (iii) Then, a most peculiar phenomenon unfolds: The strategies present in the population diversify and give rise to a "cloud" of tinkering individuals who each tries out a different strategy, and this process continues unchecked as long as the population's cooperation and participation levels remain balanced. Over time, however, imbalances build up as a consequence of random drift and there is a sudden and abrupt collapse of the strategy-diversity cloud. The process then repeats again in a cyclic manner. To understand the three aforementioned phenomena, we investigate the system analytically using adaptive-dynamics techniques. Our analysis casts light on the mechanisms which underpin the unexpected and surprising evolutionary dynamics.
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