Understanding Cooperative Behavior Based on the Coevolution of Game Strategy and Link Weight

Cooperation dynamics of prisoner's dilemma games on an evolutionary weighted network with heterogeneous preferences

Relationships between people in real life are dynamically changed with the interaction process, and due to the heterogeneous preferences, this change is different from person to person. Based on this observation, we propose a new spatial and weighted prisoner's dilemma game model with heterogeneous individuals. Two types of tags, namely, tag-F (concerned about social fairness) and tag-W (concerned about personal well-being), are introduced to describe individuals' different preferences. The link weights indicating the interaction strength between individuals are updated based on different rules that depend on their tags. Through simulations, we verify that a large link weight control factor and a high proportion of tag-F individuals favor the emergence and persistence of cooperation. In addition, an increase in the link weight sensitivity factor favors the evolution of cooperation when the link weight control factor is small. Moreover, while the level of cooperation increases with the proportion of tag-F type in the population, contrary to our intuition, when the population consists entirely of tag-F individuals, in some cases, cooperation cannot reach a higher level compared with the situation when they are mixed with tag-W type. However, at high dilemma intensities, cooperators emerge only when the entire population consists of tag-F type. These results may provide some new insights into the impact of the evolutionary weighted network with heterogeneous preferences on collective cooperative behavior.

Complex networks identification using Bayesian model with independent Laplace prior

Identification of complex networks from limited and noise contaminated data is an important yet challenging task, which has attracted researchers from different disciplines recently. In this paper, the underlying feature of a complex network identification problem was analyzed and translated into a sparse linear programming problem. Then, a general framework based on the Bayesian model with independent Laplace prior was proposed to guarantee the sparseness and accuracy of identification results after analyzing influences of different prior distributions. At the same time, a three-stage hierarchical method was designed to resolve the puzzle that the Laplace distribution is not conjugated to the normal distribution. Last, the variational Bayesian was introduced to improve the efficiency of the network reconstruction task. The high accuracy and robust properties of the proposed method were verified by conducting both general synthetic network and real network identification tasks based on the evolutionary game dynamic. Compared with other five classical algorithms, the numerical experiments indicate that the proposed model can outperform these methods in both accuracy and robustness.

Direct reciprocity and model-predictive rationality explain network reciprocity over social ties

Since M. A. Nowak & R. May’s (1992) influential paper, limiting each agent’s interactions to a few neighbors in a network of contacts has been proposed as the simplest mechanism to support the evolution of cooperation in biological and socio-economic systems. The network allows cooperative agents to self-assort into clusters, within which they reciprocate cooperation. This (induced) network reciprocity has been observed in several theoreticalmodels and shown to predict the fixation of cooperation under a simple rule: the benefit produced by an act of cooperation must outweigh the cost of cooperating with all neighbors. However, the experimental evidence among humans is controversial: though the rule seems to be confirmed, the underlying modeling assumptions are not. Specifically, models assume that agents update their strategies by imitating better performing neighbors, even though imitation lacks rationality when interactions are far from all-to-all. Indeed, imitation did not emerge in experiments. What did emerge is that humans are conditioned by their own mood and that, when in a cooperative mood, they reciprocate cooperation. To help resolve the controversy, we design a model in which we rationally confront the two main behaviors emerging from experiments—reciprocal cooperation and unconditional defection—in a networked prisoner’s dilemma. Rationality is introduced by means of a predictive rule for strategy update and is bounded by the assumed model society. We show that both reciprocity and a multi-step predictive horizon are necessary to stabilize cooperation, and sufficient for its fixation, provided the game benefit-to-cost ratio is larger than a measure of network connectivity. We hence rediscover the rule of network reciprocity, underpinned however by a different evolutionary mechanism.

Coevolution of Environmental Perception and Cooperative Behavior in Evacuation Crowd

For the evacuation crowd of social agents, environment plays a big effect on the behavior and decision of the agents. When facing the uncertain environment, the behavior and decision of agents depend heavily on the perception of environment. Therefore, the cooperation between agents and their perception of environment may coexist during evacuation. Here we establish a mechanism to analyze the coevolution between the cooperation of agents and the perception of environment. In detail, we use a regular square lattice with periodic boundaries, where two payoff matrices are used to describe two kinds of games between neighbors in the safe and dangerous environments. For individual agent, its perception can be adjusted by interacting with neighboring agents. When the environment is generally considered dangerous, the fraction of cooperative agents keeps at a high level, even if the value of b is very large. When all the agents think that the environment is safe, the fraction of cooperation will decrease as the value of b increases.

Cooperation in the spatial prisoner's dilemma game with probabilistic abstention

Research has shown that the addition of abstention as an option transforms social dilemmas to rock-paper-scissor type games, where defectors dominate cooperators, cooperators dominate abstainers (loners), and abstainers (loners), in turn, dominate defectors. In this way, abstention can sustain cooperation even under adverse conditions, although defection also persists due to cyclic dominance. However, to abstain or to act as a loner has, to date, always been considered as an independent, third strategy to complement traditional cooperation and defection. Here we consider probabilistic abstention, where each player is assigned a probability to abstain in a particular instance of the game. In the two limiting cases, the studied game reverts to the prisoner's dilemma game without loners or to the optional prisoner's dilemma game. For intermediate probabilities, we have a new hybrid game, which turns out to be most favorable for the successful evolution of cooperation. We hope this novel hybrid game provides a more realistic view of the dilemma of optional/voluntary participation.

Coevolution of teaching ability and cooperation in spatial evolutionary games

Individuals with higher reputation are able to spread their social strategies easily. At the same time, one’s reputation is changing according to his previous behaviors, which leads to completely different teaching abilities for players. To explore the effect of the teaching ability influenced by reputation, we consider a coevolutionary model in which the reputation score affects the updating rule in spatial evolutionary games. More precisely, the updating probability becomes bigger if his/her partner has a positive reputation. Otherwise, the updating probability becomes smaller. This simple design describes the influence of teaching ability on strategy adoption effectively. Numerical results focus on the proportion of cooperation under different levels of the amplitude of change of reputation and the range of reputation. For this dynamics, the fraction of cooperators presents a growth trend within a wide range of parameters. In addition, to validate the generality of this mechanism, we also employ the snowdrift game. Moreover, the evolution of cooperation on Erdős-Rényi random graph is studied for the prisoner’s dilemma game. Our results may be conducive to understanding the emergence and sustainability of cooperation during the strategy adoptions in reality.

Collapse and rescue of cooperation in evolving dynamic networks

The evolutionary dynamics of social traits depend crucially on the social structure of a population. The effects of social structure on social behaviors are well-studied, but relatively little is known about how social structure itself coevolves with social traits. Here, I study such coevolution with a simple yet realistic model of within-group social structure where social connections are either inherited from a parent or made randomly. I show that cooperation evolves when individuals make few random connections, but the presence of cooperation selects for increased rates of random connections, which leads to its collapse. Inherent costs of social connections can prevent this negative feedback, but these costs can negate some or all of the aggregate benefits of cooperation. Exogenously maintained social inheritance can mitigate the latter problem and allow cooperation to increase the average fitness of a population. These results illustrate how coevolutionary dynamics can constrain the long-term persistence of cooperation.

Coevolution of Vertex Weights Resolves Social Dilemma in Spatial Networks

In realistic social system, the role or influence of each individual varies and adaptively changes in time in the population. Inspired by this fact, we thus consider a new coevolution setup of game strategy and vertex weight on a square lattice. In detail, we model the structured population on a square lattice, on which the role or influence of each individual is depicted by vertex weight, and the prisoner’s dilemma game has been applied to describe the social dilemma of pairwise interactions of players. Through numerical simulation, we conclude that our coevolution setup can promote the evolution of cooperation effectively. Especially, there exists a moderate value of δ for each ε that can warrant an optimal resolution of social dilemma. For a further understanding of these results, we find that intermediate value of δ enables the strongest heterogeneous distribution of vertex weight. We hope our coevolution setup of vertex weight will provide new insight for the future research.

Impact of Social Reward on the Evolution of the Cooperation Behavior in Complex Networks

Social reward, as a significant mechanism explaining the evolution of cooperation, has attracted great attention both theoretically and experimentally. In this paper, we study the evolution of cooperation by proposing a reward model in network population, where a third strategy, reward, as an independent yet particular type of cooperation is introduced in 2-person evolutionary games. Specifically, a new kind of role corresponding to reward strategy, reward agents, is defined, which is aimed at increasing the income of cooperators by applying to them a social reward. Results from numerical simulations show that consideration of social reward greatly promotes the evolution of cooperation, which is confirmed for different network topologies and two evolutionary games. Moreover, we explore the microscopic mechanisms for the promotion of cooperation in the three-strategy model. As expected, the reward agents play a vital role in the formation of cooperative clusters, thus resisting the aggression of defectors. Our research might provide valuable insights into further exploring the nature of cooperation in the real world.

Culture and cooperation in a spatial public goods game

We study the coevolution of culture and cooperation by combining the Axelrod model of cultural dissemination with a spatial public goods game, incorporating both noise and social influence. Both participation and cooperation in public goods games are conditional on cultural similarity. We find that a larger "scope of cultural possibilities" in the model leads to the survival of cooperation, when noise is not present, and a higher probability of a multicultural state evolving, for low noise rates. High noise rates, however, lead to both rapid extinction of cooperation and collapse into cultural "anomie," in which stable cultural regions fail to form. These results suggest that cultural diversity can actually be beneficial for the evolution of cooperation, but that cultural information needs to be transmitted accurately in order to maintain both coherent cultural groups and cooperation.