Short versus long term benefits and the evolution of cooperation in the prisoner's dilemma game

Variation in season length and development time is sufficient to drive the emergence and coexistence of social and solitary behavioural strategies

Season length and its associated variables can influence the expression of social behaviours, including the occurrence of eusociality in insects. Eusociality can vary widely across environmental gradients, both within and between different species. Numerous theoretical models have been developed to examine the life history traits that underlie the emergence and maintenance of eusociality, yet the impact of seasonality on this process is largely uncharacterized. Here, we present a theoretical model that incorporates season length and offspring development time into a single, individual-focused model to examine how these factors can shape the costs and benefits of social living. We find that longer season lengths and faster brood development times are sufficient to favour the emergence and maintenance of a social strategy, while shorter seasons favour a solitary one. We also identify a range of season lengths where social and solitary strategies can coexist. Moreover, our theoretical predictions are well matched to the natural history and behaviour of two flexibly eusocial bee species, suggesting that our model can make realistic predictions about the evolution of different social strategies. Broadly, this work reveals the crucial role that environmental conditions can have in shaping social behaviour and its evolution and it underscores the need for further models that explicitly incorporate such variation to study the evolutionary trajectories of eusociality.

Variation in season length and development time is sufficient to drive the emergence and coexistence of social and solitary behavioral strategies

Season length and its associated variables can influence the expression of social behaviors, including the occurrence of eusociality in insects. Eusociality can vary widely across environmental gradients, both within and between different species. Numerous theoretical models have been developed to examine the life history traits that underlie the emergence and maintenance of eusociality, yet the impact of seasonality on this process is largely uncharacterized. Here, we present a theoretical model that incorporates season length and offspring development time into a single, individual-focused model to examine how these factors can shape the costs and benefits of social living. We find that longer season lengths and faster brood development times are sufficient to favor the emergence and maintenance of a social strategy, while shorter seasons favor a solitary one. We also identify a range of season lengths where social and solitary strategies can coexist. Moreover, our theoretical predictions are well-matched to the natural history and behavior of two flexibly-eusocial bee species, suggesting our model can make realistic predictions about the evolution of different social strategies. Broadly, this work reveals the crucial role that environmental conditions can have in shaping social behavior and its evolution and underscores the need for further models that explicitly incorporate such variation to study evolutionary trajectories of eusociality.

Universal scaling for the dilemma strength in evolutionary games

Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.

Defection and extortion as unexpected catalysts of unconditional cooperation in structured populations

We study the evolution of cooperation in the spatial prisoner's dilemma game, where besides unconditional cooperation and defection, tit-for-tat, win-stay-lose-shift and extortion are the five competing strategies. While pairwise imitation fails to sustain unconditional cooperation and extortion regardless of game parametrization, myopic updating gives rise to the coexistence of all five strategies if the temptation to defect is sufficiently large or if the degree distribution of the interaction network is heterogeneous. This counterintuitive evolutionary outcome emerges as a result of an unexpected chain of strategy invasions. Firstly, defectors emerge and coarsen spontaneously among players adopting win-stay-lose-shift. Secondly, extortioners and players adopting tit-for-tat emerge and spread via neutral drift among the emerged defectors. And lastly, among the extortioners, cooperators become viable too. These recurrent evolutionary invasions yield a five-strategy phase that is stable irrespective of the system size and the structure of the interaction network, and they reveal the most unexpected mechanism that stabilizes extortion and cooperation in an evolutionary setting.

Swarm intelligence inspired shills and the evolution of cooperation

Many hostile scenarios exist in real-life situations, where cooperation is disfavored and the collective behavior needs intervention for system efficiency improvement. Towards this end, the framework of soft control provides a powerful tool by introducing controllable agents called shills, who are allowed to follow well-designed updating rules for varying missions. Inspired by swarm intelligence emerging from flocks of birds, we explore here the dependence of the evolution of cooperation on soft control by an evolutionary iterated prisoner's dilemma (IPD) game staged on square lattices, where the shills adopt a particle swarm optimization (PSO) mechanism for strategy updating. We demonstrate that not only can cooperation be promoted by shills effectively seeking for potentially better strategies and spreading them to others, but also the frequency of cooperation could be arbitrarily controlled by choosing appropriate parameter settings. Moreover, we show that adding more shills does not contribute to further cooperation promotion, while assigning higher weights to the collective knowledge for strategy updating proves a efficient way to induce cooperative behavior. Our research provides insights into cooperation evolution in the presence of PSO-inspired shills and we hope it will be inspirational for future studies focusing on swarm intelligence based soft control.

Facilitators on networks reveal optimal interplay between information exchange and reciprocity

Reciprocity is firmly established as an important mechanism that promotes cooperation. An efficient information exchange is likewise important, especially on structured populations, where interactions between players are limited. Motivated by these two facts, we explore the role of facilitators in social dilemmas on networks. Facilitators are here mirrors to their neighbors-they cooperate with cooperators and defect with defectors-but they do not participate in the exchange of strategies. As such, in addition to introducing direct reciprocity, they also obstruct information exchange. In well-mixed populations, facilitators favor the replacement and invasion of defection by cooperation as long as their number exceeds a critical value. In structured populations, on the other hand, there exists a delicate balance between the benefits of reciprocity and the deterioration of information exchange. Extensive Monte Carlo simulations of social dilemmas on various interaction networks reveal that there exists an optimal interplay between reciprocity and information exchange, which sets in only when a small number of facilitators occupy the main hubs of the scale-free network. The drawbacks of missing cooperative hubs are more than compensated for by reciprocity and, at the same time, the compromised information exchange is routed via the auxiliary hubs with only marginal losses in effectivity. These results indicate that it is not always optimal for the main hubs to become leaders of the masses, but rather to exploit their highly connected state to promote tit-for-tat-like behavior.

Neurogenomics of behavioral plasticity

Across animals, there is remarkable diversity in behavior. Modern genomic approaches have made it possible to identify the molecular underpinnings of varied behavioral phenotypes. By examining species with plastic phenotypes we have begun to understand the dynamic and flexible nature of neural transcriptomes and identified gene modules associated with variation in social and reproductive behaviors in diverse species. Importantly, it is becoming increasingly clear that some candidate genes and gene networks are involved in complex social behaviors across even divergent species, yet few comparative transcriptomics studies have been conducted that examine a specific behavior across species. We discuss the implications of a range of important and insightful studies that have increased our understanding of the neurogenomics of behavioral plasticity. Despite its successes, behavioral genomics has been criticized for its lack of hypotheses and causative insights. We propose here a novel avenue to overcome some of these short-comings by complementing "forward genomics" studies (i.e., from phenotype to behaviorally relevant gene modules) with a "reverse genomics" approach (i.e., manipulating novel gene modules to examine effects on behavior, hormones, and the genome itself) to examine the functional causes and consequences of differential gene expression patterns. We discuss how several established approaches (such as pharmacological manipulations of a novel candidate pathway, fine scale mapping of novel candidate gene expression in the brain, or identifying direct targets of a novel transcription factor of interest) can be used in combination with the analysis of the accompanying neurogenomic responses to reveal unexpected biological processes. The integration of forward and reverse genomics will move the field beyond statistical associations and yield great insights into the neural and molecular control of social behavior and its evolution.

Influence of stochastic perturbation of both action updating and strategy updating in mixed-strategy 2×2 games on evolution of cooperation

In a mixed-strategy game framework, each agent's strategy is defined by a real number; on the other hand, in a discrete strategy game framework, only binary strategies, either cooperation or defection, are allowed. In a spatial mixed-strategy game, with respect to the process for updating action (offer), either a synchronous or an asynchronous strategy update should be presumed. This study elucidates how stochastic perturbation that results from a synchronous or an asynchronous process for updating action significantly affects the enhancement of cooperation in an evolutionary process. Especially, when a synchronous process for updating action is assumed, the extent of cooperation increases with an increase in degree.

Effect of initial fraction of cooperators on cooperative behavior in evolutionary prisoner's dilemma game

We investigate the influence of initial fraction of cooperators on the evolution of cooperation in spatial prisoner's dilemma games. Compared with the results of heterogeneous networks, we find that there is a relatively low initial fraction of cooperators to guarantee higher equilibrium cooperative level. While this interesting phenomenon is contrary to the commonly shared knowledge that higher initial fraction of cooperators can provide better environment for the evolution of cooperation. To support our outcome, we explore the time courses of cooperation and find that the whole course can be divided into two sequent stages: enduring (END) and expanding (EXP) periods. At the end of END period, thought there is a limited number of cooperator clusters left for the case of low initial setup, these clusters can smoothly expand to hold the whole system in the EXP period. However, for high initial fraction of cooperators, superfluous cooperator clusters hinder their effective expansion, which induces many remaining defectors surrounding the cooperator clusters. Moreover, through intensive analysis, we also demonstrate that when the tendency of three cooperation cluster characteristics (cluster size, cluster number and cluster shape) are consistent within END and EXP periods, the state that maximizes cooperation can be favored.

Direct reciprocity in spatial populations enhances R-reciprocity as well as ST-reciprocity

As is well-known, spatial reciprocity plays an important role in facilitating the emergence of cooperative traits, and the effect of direct reciprocity is also obvious for explaining the cooperation dynamics. However, how the combination of these two scenarios influences cooperation is still unclear. In the present work, we study the evolution of cooperation in 2×2 games via considering both spatial structured populations and direct reciprocity driven by the strategy with 1-memory length. Our results show that cooperation can be significantly facilitated on the whole parameter plane. For prisoner's dilemma game, cooperation dominates the system even at strong dilemma, where maximal social payoff is still realized. In this sense, R-reciprocity forms and it is robust to the extremely strong dilemma. Interestingly, when turning to chicken game, we find that ST-reciprocity is also guaranteed, through which social average payoff and cooperation is greatly enhanced. This reciprocity mechanism is supported by mean-field analysis and different interaction topologies. Thus, our study indicates that direct reciprocity in structured populations can be regarded as a more powerful factor for the sustainability of cooperation.

Costly advertising and the evolution of cooperation

In this paper, I investigate the co-evolution of fast and slow strategy spread and game strategies in populations of spatially distributed agents engaged in a one off evolutionary dilemma game. Agents are characterized by a pair of traits, a game strategy (cooperate or defect) and a binary ‘advertising’ strategy (advertise or don’t advertise). Advertising, which comes at a cost , allows investment into faster propagation of the agents’ traits to adjacent individuals. Importantly, game strategy and advertising strategy are subject to the same evolutionary mechanism. Via analytical reasoning and numerical simulations I demonstrate that a range of advertising costs exists, such that the prevalence of cooperation is significantly enhanced through co-evolution. Linking costly replication to the success of cooperators exposes a novel co-evolutionary mechanism that might contribute towards a better understanding of the origins of cooperation-supporting heterogeneity in agent populations.

Coevolution of quantum and classical strategies on evolving random networks

We study the coevolution of quantum and classical strategies on weighted and directed random networks in the realm of the prisoner's dilemma game. During the evolution, agents can break and rewire their links with the aim of maximizing payoffs, and they can also adjust the weights to indicate preferences, either positive or negative, towards their neighbors. The network structure itself is thus also subject to evolution. Importantly, the directionality of links does not affect the accumulation of payoffs nor the strategy transfers, but serves only to designate the owner of each particular link and with it the right to adjust the link as needed. We show that quantum strategies outperform classical strategies, and that the critical temptation to defect at which cooperative behavior can be maintained rises, if the network structure is updated frequently. Punishing neighbors by reducing the weights of their links also plays an important role in maintaining cooperation under adverse conditions. We find that the self-organization of the initially random network structure, driven by the evolutionary competition between quantum and classical strategies, leads to the spontaneous emergence of small average path length and a large clustering coefficient.

Decelerated invasion and waning-moon patterns in public goods games with delayed distribution

We study the evolution of cooperation in the spatial public goods game, focusing on the effects that are brought about by the delayed distribution of goods that accumulate in groups due to the continuous investments of cooperators. We find that intermediate delays enhance network reciprocity because of a decelerated invasion of defectors, who are unable to reap the same high short-term benefits as they do in the absence of delayed distribution. Long delays, however, introduce a risk because the large accumulated wealth might fall into the wrong hands. Indeed, as soon as the curvature of a cooperative cluster turns negative, the engulfed defectors can collect the heritage of many generations of cooperators and by doing so start a waning-moon pattern that nullifies the benefits of decelerated invasion. Accidental meeting points of growing cooperative clusters may also act as triggers for the waning-moon effect, thus linking the success of cooperators with their propensity to fail in a rather bizarre way. Our results highlight that "investing in the future" is a good idea only if that future is sufficiently near and not likely to be burdened by inflation.

Optimal interdependence between networks for the evolution of cooperation

Recent research has identified interactions between networks as crucial for the outcome of evolutionary games taking place on them. While the consensus is that interdependence does promote cooperation by means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we here address the question just how much interdependence there should be. Intuitively, one might assume the more the better. However, we show that in fact only an intermediate density of sufficiently strong interactions between networks warrants an optimal resolution of social dilemmas. This is due to an intricate interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links between the networks, and the independent formation of cooperative patterns on each individual network. Presented results are robust to variations of the strategy updating rule, the topology of interdependent networks, and the governing social dilemma, thus suggesting a high degree of universality.