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Representative simulation results for the spatial prisoner's dilemma with payoffs T = 1.3, R = 1, P = 0.1, and S = 0 after t = 200
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According to Thomas Hobbes' Leviathan [1651; 2008 (Touchstone, New York), English Ed], "the life of man [is] solitary, poor, nasty, brutish, and short," and it would need powerful social institutions to establish social order. In reality, however, social cooperation can also arise spontaneously, based on local interactions rather than centralized c...
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... range [16]. However, strategy mutations, random relocations, and other sources of stochas- ticity ("noise") can significantly challenge the formation and survival of cooperative clusters. When no mobility or undi- rected, random mobility are considered, the level of cooper- ation in the spatial games studied by us is sensitive to noise (see Figs. 1d and 3c), as favorable correlations between co- operative neighbors are destroyed. Success-driven migration, in contrast, is a robust mechanism: By leaving unfavorable neighborhoods, seeking more favorable ones, and remaining in cooperative neighborhoods, it supports cooperative clus- ters very efficiently against the destructive effects of ...
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... may be considered to reflect deficient imitation attempts or trial- and-error behavior. As a side effect, such noise leads to an independence of the finally resulting level of cooperation from the initial one at t = 0, and a qualitatively different pattern formation dynamics for the same payoff values, update rules, and initial conditions (see Fig. 1). Using the alternative Fermi update rule [22] would have been possible as well. However, re- setting strategies rather than inverting them, combined with values q much smaller than 1/2, has here the advantage of creating particularly adverse conditions for cooperation, inde- pendently of what strategy prevails. Below, we want to ...
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... case of classical spatial games with noise 1, but without a migration step, the resulting fraction of coop- erators in the PD tends to be very low. It basically reflects the fraction rq of cooperators due to strategy mutations. For r = q = 0.05, we find almost frozen configurations, in which only a small number of cooperators survive (see Fig. 1d). In the migration-only case without an imitation step, the frac- tion of cooperators changes only by strategy mutations. Even when the initial strategy distribution is uniform, one observes the formation of spatio-temporal patterns, but the patterns get almost frozen after some time (see Fig. ...
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... only a small number of cooperators survive (see Fig. 1d). In the migration-only case without an imitation step, the frac- tion of cooperators changes only by strategy mutations. Even when the initial strategy distribution is uniform, one observes the formation of spatio-temporal patterns, but the patterns get almost frozen after some time (see Fig. ...
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... is interesting that, although for the connectivity struc- ture of our PD model neither imitation only ( Fig. 1d) nor mi- gration only (Fig. 1e) can promote cooperation under noisy conditions, their combination does: Computer simulations show the formation of cooperative clusters with a few de- fectors at their boundaries (see Fig. 1f). Once cooperators are organized in clusters, they tend to have more neighbors and to reach higher payoffs on ...
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... is interesting that, although for the connectivity struc- ture of our PD model neither imitation only ( Fig. 1d) nor mi- gration only (Fig. 1e) can promote cooperation under noisy conditions, their combination does: Computer simulations show the formation of cooperative clusters with a few de- fectors at their boundaries (see Fig. 1f). Once cooperators are organized in clusters, they tend to have more neighbors and to reach higher payoffs on average, which allows them to ...
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... is interesting that, although for the connectivity struc- ture of our PD model neither imitation only ( Fig. 1d) nor mi- gration only (Fig. 1e) can promote cooperation under noisy conditions, their combination does: Computer simulations show the formation of cooperative clusters with a few de- fectors at their boundaries (see Fig. 1f). Once cooperators are organized in clusters, they tend to have more neighbors and to reach higher payoffs on average, which allows them to survive [9,10,25]. It will now have to be revealed, how success-driven migration causes the formation of clusters at all, considering the opposing noise effects. In particular, we will study, why ...
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... conditions for the spreading of cooperators from a supercritical cluster ("nucleus") can be understood by con- figurational analysis [26,28] (see Fig. S1), but the underlying argument can be both, simplified and extended: According to Fig. 6a, the level of cooperation changes when certain lines (or, more generally, certain hyperplanes) in the payoff-parameter space are crossed. These hyperplanes are all of the linear ...
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... above features-the survival of cooperation in a large parameter area of the PD, spatio- temporal pattern formation, noise-resistance, and the out- break of predominant cooperation-can be captured by con- sidering a mechanism as simple as success-driven migration: Success-driven migration destabilizes a homogeneous strategy distribution (compare Fig. 1c with 1a and Fig. 1f with 1d). This triggers the spontaneous formation of agglomeration and segregation patterns [29], where noise or diffusion would cause dispersal in the imitation-only case. The self-organized pat- terns create self-reinforcing social environments characterized by behavioral correlations, and imitation promotes the fur- ther ...
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... survival of cooperation in a large parameter area of the PD, spatio- temporal pattern formation, noise-resistance, and the out- break of predominant cooperation-can be captured by con- sidering a mechanism as simple as success-driven migration: Success-driven migration destabilizes a homogeneous strategy distribution (compare Fig. 1c with 1a and Fig. 1f with 1d). This triggers the spontaneous formation of agglomeration and segregation patterns [29], where noise or diffusion would cause dispersal in the imitation-only case. The self-organized pat- terns create self-reinforcing social environments characterized by behavioral correlations, and imitation promotes the fur- ther growth of ...
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... self-organized pat- terns create self-reinforcing social environments characterized by behavioral correlations, and imitation promotes the fur- ther growth of supercritical cooperation clusters. While each mechanism by itself tends to produce frozen spatial struc- tures, the combination of imitation and migration supports adaptive patterns (see Fig. 1f). This facilitates, for example, the regrouping of a cluster of cooperators upon invasion by a defector, which is crucial for the survival and success of coop- erators (see Fig. ...
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... It has been confirmed that complex networks, such as small-world networks [10] and scale-free networks [11], could support cooperation due to network reciprocity. So far, most previous studies assume that the motivation for imitation is payoff-based bias, i.e., individuals prefer to adopt the strategy with a higher payoff [5,12,13]. However, several studies in behavioral game theory offer alternative explanations for changes in individual behavior [14,15]. ...
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... This mechanism, which is practically an enhanced form of direct reciprocity [2], has been tested and justified by several forthcoming works [3,4,5,6,7,8] and became a starting element when different consequences of interaction topologies were studied on the evolution of cooperation [9,10,11,12]. Notably, there are certain mechanisms, like searching for a more supportive environment [13,14], avoiding toxic neighbors via migration [15,16], giving up the concept of uniform supporting and focusing on a specific neighbor [17,18,19,20], or applying interaction stochasticity toward different neighbors [21,22], which cannot be interpreted in a well-mixed population. Therefore, assuming a certain structure of interaction is inevitable for them. ...
Introducing strategy complexity into the basic conflict of cooperation and defection is a natural response to avoid the tragedy of the common state. As an intermediate approach, quasi-cooperators were recently suggested to address the original problem. In this study, we test its vitality in structured populations where players have fixed partners. Naively, the latter condition should support cooperation unambiguously via enhanced network reciprocity. However, the opposite is true because the spatial structure may provide a humbler cooperation level than a well-mixed population. This unexpected behavior can be understood if we consider that at a certain parameter interval the original prisoner's dilemma game is transformed into a snow-drift game. If we replace the original imitating strategy protocol by assuming myopic players, the spatial population becomes a friendly environment for cooperation. This observation is valid in a huge region of parameter space. This study highlights that spatial structure can reveal a new aspect of social dilemmas when strategy complexity is introduced.
... Such cooperative and fairness norms make sense for both individuals and the group from an evolutionary perspective, and a substantial body of research has demonstrated just that utility [8,77,160,[166][167][168][169][170][171]. However, this same logic cannot be applied universally to all norms and normative expectations. ...
Do social norms really matter, or are they just behavioral idiosyncrasies that become associated with a group? Social norms are generally considered as a collection of formal or informal rules, but where do these rules come from, and why do we follow them? The definition for social norm varies by field of study, and how norms are established and maintained remains substantially open to questions across the behavioral sciences. In reviewing the literature on social norms across multiple disciplines, we found that the common thread appears to be information. Here, we show that norms are not merely rules or strategies, but part of a more rudimentary social process for capturing and retaining information within a social network. We have found that the emergence of norms can be better explained as an efficient system of communicating, filtering, and preserving experiential information. By reconsidering social norms and institutions in terms of information, we show that they are not merely conventions that facilitate the coordination of social behavior. They are, instead, the objective of that social coordination and, potentially, of the evolutionary adaptation of sociality itself.
... To uncover the underlying mechanisms of how cooperative behavior evolves and persists, researchers have turned to the evolutionary game theorya powerful framework and canonical paradigm for explaining the evolution of collective cooperation [16][17][18][19][20][21]in which interactions between individuals are determined * amingli@pku.edu.cn by spatial relationships or social networks [22][23][24][25][26][27][28][29]. Traditionally, individuals are willing to change unfavorable surroundings by detecting other possible locations with higher expected payoffs, where the information that individuals rely on to make decisions is assumed to be completely true [30][31][32][33][34][35]. In reality, however, due to the proliferation of misinformation, individuals may receive false information about the alternative locations. ...
... A defector attempting to exploit a cooperator obtains T and leaves S to its opponent cooperator. Following the canonical practice [29,32,36], a single parameter T = b is employed here to depict the level of social dilemma for collective cooperation (namely R = 1, S = 0, P = 0.1), where b captures the advantages of defectors over cooperators (1 < b < 2). ...
Human societies are organized and developed through collective cooperative behaviors, in which interactions between individuals are governed by the underlying social connections. It is well known that, based on the information in their environment, individuals can form collective cooperation by strategically imitating superior behaviors and changing unfavorable surroundings in self-organizing ways. However, facing the tough situation that some humans and social bots keep spreading misinformation, we still lack the systematic investigation on the impact of such proliferation of misinformation on the evolution of social cooperation. Here we study this problem by virtue of classical evolutionary game theory. We find that misinformation generally impedes the emergence of collective cooperation compared to scenarios with completely true information, although the level of cooperation is slightly higher when the benefits provided by cooperators are reduced below a proven threshold. We further show that this possible advantage shrinks as social connections become denser, suggesting that misinformation is more detrimental to the formation of collective cooperation when 'social viscosity' is low. Our results uncover the quantitative effect of misinformation on the social cooperative behavior in the complex networked society, and pave the way for designing possible interventions to improve collective cooperation.
... Recently researchers brought this altruistic behavior of the free space to the limelight by investigating its impact on the evolution of cooperation (Nag Chowdhury et al., 2021b,a;Roy et al., 2022). Various simpler models with diverse motivations (Helbing and Yu, 2009;Nag Chowdhury et al., 2020b;Jiang et al., 2010;Nag Chowdhury et al., 2020c;Meloni et al., 2009;Sar et al., 2022;Noh and Rieger, 2004;Aktipis, 2004;Vainstein et al., 2007;Nag Chowdhury et al., 2019b;Smaldino and Schank, 2012) have been proposed to study the impact of free space on natural and human-made systems. Nevertheless, how free space's unselfish concern to benefit others than itself influences the predator-prey interaction is yet to be discovered. ...
Predator-prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely parasites. We first show that a simple predator-prey-parasite model, inspired by the classical Lotka-Volterra equations, fails to produce a stable coexistence of all three species, thus failing to provide a biologically realistic outcome. To improve this, we introduce free space as a relevant eco-evolutionary component in a new mathematical model that uses a game-theoretical payoff matrix to describe a more realistic setup. We then show that the consideration of free space stabilizes the dynamics by means of cyclic dominance that emerges between the three species. We determine the parameter regions of coexistence as well as the types of bifurcations leading to it by means of analytical derivations as well as by means of numerical simulations. We conclude that the consideration of free space as a finite resource reveals the limits of biodiversity in predator-prey-parasite interactions, and it may also help us in the determination of factors that promote a healthy biota.
... They are open to anyone, but its use prohibits the use of a different EV driver. Typically, in a CPR there is limited central steering of behaviour, which allows bottom-up cooperation strategies to emerge from individuals (Gollwitzer et al., 2018;Helbing & Yu, 2009). With growing number of stations on the street, EV charging should be considered as a network infrastructure (Helmus et al., 2019). ...
... Studies have successfully described phenomena in other socio-technical systems CPRs in which interactions between actors in the systems are important. Simulation models have pointed at the spontaneous emergence of cooperative behaviour in noisy systems where agents are success driven (Helbing & Yu, 2009). Results from this research show cluster formation of agents that are willing to help each other. ...
... Direct reciprocity is defined as an exchange between two non-related individuals on a repeated basis. Given that cooperation happens on a repeated basis, it could beneficial for an individual to cooperate in the expectation that the other will cooperate the next time as well (Helbing & Yu, 2009). Such strategies are best known in the form of the repeated prisoners' dilemma in which the so-called tit-for-tat strategy is one of the more effective strategies (Axelrod, 1980). ...
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... Common game metaphors include prisoner's 5 dilemma games [6,7], where cooperation strategy is completely defeated, and snowdrift games [8], where cooperation strategy and defection strategy coexist. On this basis, more and more factors promoting cooperation have been studied, such as reputation [9][10][11], heterogeneity [12][13][14], mobility [15][16][17] , interdependent network [18][19][20] and so on. In addition, Nowak once summarized five reciprocity mechanisms [21], including direct reciprocity [22], indirect reciprocity [23,24], kin selection [25], multi-level selection [26] and network reciprocity [27,28]. ...
... The conflict of personal profit preferences leads to the emergence of social dilemmas [18,19], in which cooperative behavior in favor of collective interests is threatened by self-interested acts of defection and disappears. Evolutionary game theory is a powerful paradigm for exploring the evolution of individual conflicts of interests [20][21][22][23][24][25], based on which some research has found that mechanisms such as rewards [26][27][28] and punishments [29][30][31], exit rights [32,33], network reciprocity [22,23,34], and migration [35][36][37] can help the establishment and maintenance of cooperation. On the other hand, explaining the evolution of cooperation based on human behavior patterns has yielded fruitful results. ...
... This means that under moderate distress intensities, a seemingly neglected tiny cooperative cluster can become a core attraction for population aggregation under adaptive migration. The tiny cooperative clusters may form as a result of self-organization of cooperators, or behavioral noise [37]. ...
Understanding population segregation and aggregation is a critical topic in social science. However, the mechanisms behind segregation are not well understood, especially in the context of conflicting profits. Here, in the context of evolutionary game theory, we study segregation by extending the prisoner's dilemma game to mobile populations. In the extended model, individuals' types are distinguished by their strategies, which may change adaptively according to their associated payoffs. In addition, individuals' migration decisions are determined by the Q-learning algorithm. We find that, on the one hand, such a simple extension allows the formation of three different types of spontaneous segregation: (i) environmentally selective segregation; (ii) exclusionary segregation; and (iii) subgroup segregation. On the other hand, adaptive migration enhances network reciprocity and enables the dominance of cooperation in a dense population. The formation of these types of segregation and the enhanced network reciprocity are related to individuals' peer preference and profit preference. Our findings shed light on the significance of adaptive migration in self-organization processes and enrich our understanding of the formation processes of segregation in evolving populations.
... But how such a control is achieved when conflicting constraints arise? Previous work has explored the dynamics of cooperation under game-theory approximations [11,38] including those experiencing noisy conditions [39]. In other studies, the use of neural agents allowed to explore the emergence of simple cooperative strategies [40] and the interplay between cooperation and social intelligence [41]. ...
Humans have been able to tackle biosphere complexities by acting as ecosystem engineers, profoundly changing the flows of matter, energy and information. This includes major innovations that allowed to reduce and control the impact of extreme events. Modelling the evolution of such adaptive dynamics can be challenging given the potentially large number of individual and environmental variables involved. This paper shows how to address this problem by using fire as the source of external, bursting and wide fluctuations. Fire propagates on a spatial landscape where a group of agents harvest and exploit trees while avoiding the damaging effects of fire spreading. The agents need to solve a conflict to reach a group-level optimal state: while tree harvesting reduces the propagation of fires, it also reduces the availability of resources provided by trees. It is shown that the system displays two major evolutionary innovations that end up in an ecological engineering strategy that favours high biomass along with the suppression of large fires. The implications for potential A.I. management of complex ecosystems are discussed.
... There are mainly two kinds of motivation driven migration. One is success-driven migration where individuals would prefer to choose a vacancy that offers a higher payoff than their current location as the target habitat [13], [14]. Another example is aspiration-driven migration where an individual maybe migrate to another site from his current position when his obtained payoff cannot meet his aspiration [15]- [17] or expectation [18], [19]. ...
... Each individual is assigned a cooperation strategy or a defection strategy with equal probability. It is worth noting that some solitary cooperators can sustain along around defectors, in sharp contrast with almost all previous surveys [13], [15], [16], [18]- [20]. ...
... Notably, a small number of cooperative strategies survive by forming sparse clusters, even if cooperation loses a large area of territory in this period. Not only that, it is reflected that some solitary cooperators can even survive alone around defectors, contrary to most existing results [13], [15], [16], [18]- [20]. And we attribute this phenomenon to the neighbor retention effect. ...
