Extensive behavioral experiments reveal that conditional cooperation is a prevalent phenomenon. Previous game-theoretical studies have predominantly relied on hard-manner models, where cooperation is triggered only upon reaching a specific threshold. However, this approach contrasts with the observed flexibility of human behaviors, where individuals adapt their strategies dynamically based on their surroundings. To capture this adaptability, we introduce a soft form of conditional cooperation by integrating the Q-learning algorithm from reinforcement learning. In this form, players not only reciprocate mutual cooperation but may also defect in highly cooperative environments or cooperate in less cooperative settings to maximize rewards. To explore the effects of hard and soft conditional cooperators, we examine their interactions in two scenarios: structural mixture (SM) and probabilistic mixture (PM), where the two behavioral modes are fixed and probabilistically adopted, respectively. In SM, hard conditional cooperators enhance cooperation when the threshold is low but hinder it otherwise. Surprisingly, in PM, the cooperation prevalence exhibits two first-order phase transitions as the probability is varied, leading to high, low, and vanishing levels of cooperation. Analysis of Q-tables offers insights into the "psychological shifts" of soft conditional cooperators and the overall evolutionary dynamics. Model extensions confirm the robustness of our findings. These results highlight the novel complexities arising from the diversity of conditional cooperators.
Despite the wealth of empirical and theoretical studies, the origin and maintenance of cooperation is still an evolutionary riddle. In this context, ecological life-history traits which affect the efficiency of selection may play a role, though these are often ignored. We consider here species such as bacteria, fungi, invertebrates and plants which exhibit resting stages in the form of a quiescent state or a seedbank. When quiescent, individuals are inactive and reproduce upon activation, while under seed bank parents produce offspring remaining dormant for different amount of time. We assume …
Predicting success of cooperators across arbitrary heterogeneous environmental landscapes
School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran（基础科学研究所生物科学学院）；University of Minnesota, Minneapolis, MN, USA（明尼苏达大学）；Institute of Science and Technology Austria, Klosterneuburg, Austria（奥地利科学技术研究所）
Whether or not cooperation is favored in evolutionary games on graphs depends on the population structure and spatial properties of the interaction network. Population structures can be expressed as configurations. Such configurations extend scenarios with a single cooperator among defectors to any number of cooperators and any arrangement of cooperators and defectors. Thus, as a single cooperator can be interpreted as a lone mutant, the discussion about fixation properties based on configurations also applies to multiple mutants. For interaction networks modeled as regular graphs and for weak…
Cooperators forgo their interest to benefit others. Thus cooperation should not be favored by natural selection. It challenges the evolutionists, since cooperation is widespread. As one of the resolutions, information spreading has been revealed to play a key role in the emergence of cooperation. Individuals, however, are typically assumed to be passive in the information spreading. Here we assume that individuals are active to spread the information via self-recommendation. Individuals with higher intensities of self-recommendation are likely to have more neighbors. We find that i) eloquent c…
Range expansion is a universal process in biological systems, and therefore plays a part in biological evolution. Using a quantitative individual-based method based on the stochastic process, we identify that enhancing the inherent self-proliferation advantage of cooperators relative to defectors is a more effective channel to promote the evolution of cooperation in range expansion than weakening the benefit acquisition of defectors from cooperators. With this self-proliferation advantage, cooperators can rapidly colonize virgin space and establish spatial segregation more readily, which acts …
Consider a cooperation game on a spatial network of habitat patches, where players can relocate between patches if they judge the local conditions to be unfavorable. In time, the relocation events may lead to a homogeneous state where all patches harbor the same relative densities of cooperators and defectors or they may lead to self-organized patterns, where some patches become safe havens that maintain an elevated cooperator density. Here we analyze the transition between these states mathematically. We show that safe havens form once a certain threshold in connectivity is crossed. This thre…
Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecological…
In recent years, there has been growing interest in studying evolutionary games with environmental feedback. Previous studies exclusively focus on two-player games. However, extension to multi-player game is needed to study problems such as microbial cooperation and crowdsourcing collaborations. Here, we study coevolutionary public goods games where strategies coevolve with the multiplication factors of group cooperation. Asymmetry can arise in such environmental feedback, where games organized by focal cooperators may have a different efficiency than the ones by defectors. Our analysis shows …
We study the evolution of cooperation as a birth-death process in spatially extended populations. The benefit from the altruistic behavior of a cooperator is implemented by decreasing the death rate of its direct neighbors. The cost of cooperation is the increase of a cooperator's death rate proportional to the number of its neighbors. When cooperation has higher cost than benefit, cooperators disappear. Then the dynamics reduces to the contact process with defectors as the single particle type. Increasing the benefit-cost ratio above 1, the extinction transition of the contact process splits …
The evolution of cooperation has remained an important problem in evolutionary theory and social sciences. In this regard, a curious question is why consistent cooperative and defective personalities exist and if they serve a role in the evolution of cooperation? To shed light on these questions, here, I consider a population of individuals who possibly play two consecutive rounds of public goods game, with different enhancement factors. Importantly, individuals have independent strategies in the two rounds. However, their strategy in the first round affects the game they play in the second ro…
Hierarchical invasion of cooperation in complex networks
合作的出现和生存是科学中仍然存在的最困难的问题之一。惩罚的存在、有限系统中的波动、重复的相互作用和威望的形成等几个因素都可能有助于解释自然和社会系统中合作的反直觉流行。互动网络的特性也被认为是有利于合作者持久性的一个因素。在这里，我们考虑在复杂的拓扑结构的合作行为的入侵动力学。从具有给定连接数（度）$k_0$的节点开始执行完全被叛逃者占据的异构网络的入侵。然后，系统内的囚徒困境的游戏和结果进行了分析，作为一个功能的$k_0$和程度$k$的节点采用合作。使用数值和分析方法进行，我们的研究结果表明，入侵收益优先以下的层次顺序的节点，从那些具有较高程度的那些具有较低程度。然而，只有当最初的合作者数量足够多，形成一个集群，合作才能传播开来，合作的入侵才会成功。这意味着初始条件必须是高度数和高数值度之间的适当平衡，这通常在可能的情况下发生在$k_0$的中间值。这些发现具有潜在的应用，因为它们表明，为了促进复杂网络上的合作行为，应该感染合作者\emph{high but not too high}度节点。
Diffusion-induced instabilities promote cooperation in eco-evolutionary networks
Bagchi School of Public Health, Ahmedabad University（艾哈迈达巴德大学巴吉公共卫生学院）；Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata（印度科学教育与研究学院加尔各答分校物理科学系）；Department of Mathematics and Namur Institute for Complex Systems - naXys, University of Namur（南纳尔大学数学与南纳尔复杂系统研究所-naXys）；Faculty of Natural Sciences and Mathematics, University of Maribor（马里博尔大学自然科学与数学学院）；Community Healthcare Center Dr. Adolf Drolc Maribor（马里博尔阿道夫·德罗尔克博士社区健康中心）；Department of Physics, Kyung Hee University（庆熙大学物理系）；University College, Korea University（韩国大学综合研究生院）；Physics and Applied Mathematics Unit, Indian Statistical Institute（印度统计物理学与应用数学单元）
Spatial structure is one of the simplest and most studied ecological factors that affect the evolution of cooperation. It has been shown that spatial reciprocity promotes cooperation due to the formation of cooperative clusters, which provide mutual support against defectors. The usual assumption is that of constant population size, where no density-related effect is possible. Here, we extend the investigation of density-related effects on the evolution of cooperation. We integrate evolutionary game theory to the Lattice Lotka-Volterra Model. In our model, the birth rate depends on the local d…
We study the evolutionary dynamics of the prisoner's dilemma game in which cooperators and defectors interact with another actor type called exiters. Rather than being exploited by defectors, exiters exit the game in favour of a small payoff. We find that this simple extension of the game allows cooperation to flourish in well-mixed populations when iterations or reputation are added. In networked populations, however, the exit option is less conducive to cooperation. Instead, it enables the coexistence of cooperators, defectors, and exiters through cyclic dominance. Other outcomes are also po…
Cooperation is the backbone of modern human societies, making it a priority to understand how successful cooperation-sustaining mechanisms operate. Cyclic dominance, a non-transitive setup comprising at least three strategies wherein the first strategy overrules the second which overrules the third which, in turn, overrules the first strategy, is known to maintain bio-diversity, drive competition between bacterial strains, and preserve cooperation in social dilemmas. Here, we present a novel route to cyclic dominance in voluntary social dilemmas by adding to the traditional mix of cooperators,…
Game theory deals with strategic interactions among players and evolutionary game dynamics tracks the fate of the players' populations under selection. In this paper, we consider the replicator equation for two-player-two-strategy games involving cooperators and defectors. We modify the equation to include the effect of mutation and also delay that corresponds either to the delayed information about the population state or in realizing the effect of interaction among players. By focusing on the four exhaustive classes of symmetrical games -- the Stag Hunt game, the Snowdrift game, the Prisoner…
This article considers a mechanism to explain the emergence and evolution of social cooperation. Selfish individuals tend to benefit themselves, which makes it hard for the maintenance of cooperation between unrelated individuals. We propose and validate that a smart group strategy can effectively facilitate the evolution of cooperation, provided cooperators spatially align whilst cooperating at a new level of alliance. The general evolutionary model presented here shows that a non-kin selection effect is a possible cause for cooperation between unrelated individuals and highlights that non-ki…
ETH Zürich（苏黎世联邦理工学院）；Complexity Science Hub Vienna（维也纳复杂性科学中心）；University of Maribor（马里博尔大学）；China Medical University Hospital, China Medical University（中国医药大学附设医院，中国医药大学）；Alma Mater Europaea（欧洲母校大学）
In a non-sustainable, "over-populated" world, what might the use of nanotechnology-based targeted, autonomous weapons mean for the future of humanity? In order to gain some insights, we make a simplified game-theoretical thought experiment. We consider a population where agents play the public goods game, and where in parallel an epidemic unfolds. Agents that are infected defectors are killed with a certain probability and replaced by susceptible cooperators. We show that such "nanowars", even if aiming to promote good behavior and planetary health, fail not only to promote cooperation, but th…
Finding ways to overcome the temptation to exploit one another is still a challenge in behavioural sciences. In the framework of evolutionary game theory, punishing strategies are frequently used to promote cooperation in competitive environments. Here, we introduce altruistic punishers in the spatial public goods game. This strategy acts as a cooperator in the absence of defectors, otherwise it will punish all defectors in their vicinity while bearing a cost to do so. We observe three distinct behaviours in our model: i) in the absence of punishers, cooperators (who don't punish defectors) ar…
We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. Using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak selection to favor cooperation over defection on any regular graph with $N \leq 14$ vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of certain length is a good predictor for the values of the structure coefficient, and thus …
