Evolutionary multigame with conformists and profiteers based on dynamic complex networks

A memory-based spatial evolutionary game with the dynamic interaction between learners and profiteers

Spatial evolutionary games provide a valuable framework for elucidating the emergence and maintenance of cooperative behaviors. However, most previous studies assume that individuals are profiteers and neglect to consider the effects of memory. To bridge this gap, in this paper, we propose a memory-based spatial evolutionary game with dynamic interaction between learners and profiteers. Specifically, there are two different categories of individuals in the network, including profiteers and learners with different strategy updating rules. Notably, there is a dynamic interaction between profiteers and learners, i.e., each individual has the transition probability between profiteers and learners, which is portrayed by a Markov process. Besides, the payoff of each individual is not only determined by a single round of the game but also depends on the memory mechanism of the individual. Extensive numerical simulations validate the theoretical analysis and uncover that dynamic interactions between profiteers and learners foster cooperation, memory mechanisms facilitate the emergence of cooperative behaviors among profiteers, and increasing the learning rate of learners promotes a rise in the number of cooperators. In addition, the robustness of the model is verified through simulations across various network sizes. Overall, this work contributes to a deeper understanding of the mechanisms driving the formation and evolution of cooperation.

Co-evolution of heterogeneous cognition in spatial snowdrift game with asymmetric cost

The emergence of the evolutionary game on complex networks provides a fresh framework for studying cooperation behavior between complex populations. Numerous recent progress has been achieved in studying asymmetric games. However, there is still a substantial need to address how to flexibly express the individual asymmetric nature. In this paper, we employ mutual cognition among individuals to elucidate the asymmetry inherent in their interactions. Cognition arises from individuals' subjective assessments and significantly influences their decision-making processes. In social networks, mutual cognition among individuals is a persistent phenomenon and frequently displays heterogeneity as the influence of their interactions. This unequal cognitive dynamic will, in turn, influence the interactions, culminating in asymmetric outcomes. To better illustrate the inter-individual cognition in asymmetric snowdrift games, the concept of favor value is introduced here. On this basis, the evolution of cognition and its relationship with asymmetry degree are defined. In our simulation, we investigate how game cost and the intensity of individual cognitive changes impact the cooperation frequency. Furthermore, the temporal evolution of individual cognition and its variation under different parameters was also examined. The simulation results reveal that the emergence of heterogeneous cognition effectively addresses social dilemmas, with asymmetric interactions among individuals enhancing the propensity for cooperative choices. It is noteworthy that distinctions exist in the rules governing cooperation and cognitive evolution between regular networks and Watts-Strogatz small-world networks. In light of this, we deduce the relationship between cognition evolution and cooperative behavior in co-evolution and explore potential factors influencing cooperation within the system.

The evolution and social cost of herding mentality promote cooperation

Herding behavior has a social cost for individuals not following the herd, influencing human decision-making. This work proposes including a social cost derived from herding mentality into the payoffs of pairwise game interactions. We introduce a co-evolutionary asymmetric model with four individual strategies (cooperation vs. defection and herding vs. non-herding) to understand the co-emergence of herding behavior and cooperation. Computational experiments show how including herding costs promotes cooperation by increasing the parameter space under which cooperation persists. Results demonstrate a synergistic relationship between the emergence of cooperation and herding mentality: the highest cooperation is achieved when the herding mentality also achieves its highest level. Finally, we study different herding social costs and its relationship to cooperation and herding evolution. This study points to new social mechanisms, related to conformity-driven imitation behavior, that help to understand how and why cooperation prevails in human groups.

When costly migration helps to improve cooperation

Motion is a typical reaction among animals and humans trying to reach better conditions in a changing world. This aspect has been studied intensively in social dilemmas where competing players' individual and collective interests are in conflict. Starting from the traditional public goods game model, where players are locally fixed and unconditional cooperators or defectors are present, we introduce two additional strategies through which agents can change their positions of dependence on the local cooperation level. More importantly, these so-called sophisticated players should bear an extra cost to maintain their permanent capacity to evaluate their neighborhood and react accordingly. Hence, four strategies compete, and the most successful one can be imitated by its neighbors. Crucially, the introduction of costly movement has a highly biased consequence on the competing main strategies. In the majority of parameter space, it is harmful to defectors and provides a significantly higher cooperation level when the population is rare. At an intermediate population density, which would be otherwise optimal for a system of immobile players, the presence of mobile actors could be detrimental if the interaction pattern changes slightly, thereby blocking the optimal percolation of information flow. In this parameter space, sophisticated cooperators can also show the co-called Moor effect by first avoiding the harmful vicinity of defectors; they subsequently transform into an immobile cooperator state. Hence, paradoxically, the additional cost of movement could be advantageous to reach a higher general income, especially for a rare population when subgroups would be isolated otherwise.

Spatial evolution of cooperation with variable payoffs

In the evolution of cooperation, the individuals' payoffs are commonly random in real situations, e.g., the social networks and the economic regions, leading to unpredictable factors. Therefore, there are chances for each individual to obtain the exceeding payoff and risks to get the low payoff. In this paper, we consider that each individual's payoff follows a specific probability distribution with a fixed expectation, where the normal distribution and the exponential distribution are employed in our model. In the simulations, we perform the models on the weak prisoner's dilemmas (WPDs) and the snowdrift games (SDGs), and four types of networks, including the hexagon lattice, the square lattice, the small-world network, and the triangular lattice are considered. For the individuals' normally distributed payoff, we find that the higher standard deviation usually inhibits the cooperation for the WPDs but promotes the cooperation for the SDGs. Besides, with a higher standard deviation, the cooperation clusters are usually split for the WPDs but constructed for the SDGs. For the individuals' exponentially distributed payoff, we find that the small-world network provides the best condition for the emergence of cooperators in WPDs and SDGs. However, when playing SDGs, the small-world network allows the smallest space for the pure cooperative state while the hexagon lattice allows the largest.

Prisoner's Dilemma Game with Cooperation-Defection Dominance Strategies on Correlational Multilayer Networks

As multilayer networks are widely applied in modern society, numerous studies have shown the impact of a multilayer network structure and the network nature on the proportion of cooperators in the network. In this paper, we use Barabási-Albert scale-free networks (BA) and Watts and Strogatz networks (WS) to build a multilayer network structure, and we propose a new strategy-updating rule called "cooperation-defection dominance", which can be likened to dominant and recessive traits in biogenetics. With the newly constructed multilayer network structure and the strategy-updating rules, based on the simulation results, we find that in the BA-BA network, the cooperation dominance strategy can make the networks with different rs show a cooperative trend, while the defection dominance strategy only has an obvious effect on the network cooperation with a larger r. When the BA network is connected to the WS network, we find that the effect of strategy on the proportion of cooperators in the network decreases, and the main influencing factor is the structure of the network. In the three-layer network, the cooperation dominance strategy has a greater impact on the BA network, and the proportion of the cooperators is enhanced more than under the natural evolution strategy, but the promotion effect is still smaller than that of the two-layer BA network because of the WS network. Under the defection dominance strategy, the WS layer appears different from the first two strategies, and we conclude through simulation that when the payoff parameter is at the middle level, its cooperator proportion will be suppressed, and we deduce that the proportion of cooperators and defectors, as well as the payoff, play an important role.

The Polarization of the Coupling Strength of Interdependent Networks Stimulates Cooperation

We introduce a mixed network coupling mechanism and study its effects on how cooperation evolves in interdependent networks. This mechanism allows some players (conservative-driven) to establish a fixed-strength coupling, while other players (radical-driven) adjust their coupling strength through the evolution of strategy. By means of numerical simulation, a hump-like relationship between the level of cooperation and conservative participant density is revealed. Interestingly, interspecies interactions stimulate polarization of the coupling strength of radical-driven players, promoting cooperation between two types of players. We thus demonstrate that a simple mixed network coupling mechanism substantially expands the scope of cooperation among structured populations.

Defectors in bad circumstances possessing higher reputation can promote cooperation

In nature and human society, social relationships and behavior patterns are usually unpredictable. In any interaction, individuals will constantly have to deal with prior uncertainty. The concept of "reputation" can provide some information to mitigate such uncertainty. In previous studies, researchers have considered that only cooperators are able to maintain a high reputation; no matter the circumstances of a defector, they are classified as a faithless individual. In reality, however, some individuals will be forced to defect to protect themselves against exploitation. Therefore, it makes sense that defectors in bad circumstances could also obtain higher reputations, and cooperators can maintain higher reputations in comfortable circumstances. In this work, the reputations of individuals are calculated using the fraction of their neighbors who have the same strategy. In this way, some defectors in a population may obtain higher reputations than some cooperators. We introduce this reputation rule using heterogeneous investments in public goods games. Our numerical simulation results indicate that this reputation rule and heterogeneous investments can better stimulate cooperation. Additionally, stronger investment heterogeneity can further increase the level of cooperation. To explain this phenomenon, dynamical evolution is observed in Monte Carlo simulations. We also investigated the effects of the noise intensity of the irrational population and the original proportion of cooperation in the population. The robustness of this cooperation model was also considered with respect to the network structure and total investment, and we found that the conclusions remained the same.

Small group size promotes more egalitarian societies as modeled by the hawk-dove game

The social organization of groups varies greatly across primate species, ranging from egalitarian to despotic. Moreover, the typical or average size of groups varies greatly across primate species. Yet we know little about how group size affects social organization across primate species. Here we used the hawk-dove game (HDG) to model the evolution of social organization as a function of maximum group size and used the evolved frequency of hawks as a measure of egalitarian/despotism in societies. That is, the lower the frequency of hawks, the more egalitarian a society is, and the higher the frequency of hawks, the more despotic it is. To do this, we built an agent-based model in which agents live in groups and play the HDG with fellow group members to obtain resources to reproduce offspring. Offspring inherit the strategy of their parent (hawk or dove) with a low mutation rate. When groups reach a specified maximum size, they are randomly divided into two groups. We show that the evolved frequency of hawks is dramatically lower for relatively small maximum group sizes than predicted analytically for the HDG. We discuss the relevance of group size for understanding and modeling primate social systems, including the transition from hunter-gather societies to agricultural societies of the Neolithic era. We conclude that group size should be included in our theoretical understanding of the organization of primate social systems.