Cascade of elimination and emergence of pure cooperation in coevolutionary games on networks

Autonomy promotes the evolution of cooperation in prisoner's dilemma

Population structure has been widely reported to foster cooperation in spatially structured populations, where individuals interact with all of their network neighbors defined by the spatial structure in each generation. However, most results rely on the assumption that individuals strictly interact with all of their neighbors during evolution. In reality, human beings, with sophisticated psychology, are willing to interact with some of their neighbors from time to time. Thus, individuals may not play games with all neighbors due to their psychological factors. Here we investigate how the autonomy, one of the basic psychological needs, affects the fate of cooperators in various social networks. By constructing a dynamical effective network, we find that the introduction of autonomy favors cooperative behavior. Further systematical studies by eliminating heterogeneity and the dynamic characteristics of the network reveal that autonomy plays a pivotal role in the evolution of cooperation. Moreover, we find that a moderate effective network degree, defined by the product of the original network degree and the level of autonomy, maximizes the cooperation on networks connecting individuals with fixed neighbors. Our results offer a possible way for organizations to improve individuals' cooperation and shed light on the importance of individuals' psychology on the evolution of cooperation.

Coevolution of public goods game and networks based on survival of the fittest

We introduce a random strategy update rule for the evolutionary public goods game on networks based on survival of the fittest. A survival cost parameter is introduced to public goods game. Players whose payoffs are below the survival cost will be deleted from the network. The same number of new nodes are randomly connected to the network and randomly designated cooperation or defection. Numerical results show that cooperation can flourish if the multiplication factor of the public goods game is greater than the network degree. We present a simple analytical method to explain this result. The fraction of cooperators reaches the maximum for a suitable survival cost. Furthermore, the initial random network has evolved into a heterogeneous network which facilitates the emergence of the cooperation. Our work could be helpful to understand how natural selection favors cooperation. It suggests a new method to investigate the impact of the survival cost on the evolution of cooperation.

Coevolutionary dynamics of phenotypic diversity and contingent cooperation

Phenotypic diversity is considered beneficial to the evolution of contingent cooperation, in which cooperators channel their help preferentially towards others of similar phenotypes. However, it remains largely unclear how phenotypic variation arises in the first place and thus leads to the construction of phenotypic complexity. Here we propose a mathematical model to study the coevolutionary dynamics of phenotypic diversity and contingent cooperation. Unlike previous models, our model does not assume any prescribed level of phenotypic diversity, but rather lets it be an evolvable trait. Each individual expresses one phenotype at a time and only the phenotypes expressed are visible to others. Moreover, individuals can differ in their potential of phenotypic variation, which is characterized by the number of distinct phenotypes they can randomly switch to. Each individual incurs a cost proportional to the number of potentially expressible phenotypes so as to retain phenotypic variation and expression. Our results show that phenotypic diversity coevolves with contingent cooperation under a wide range of conditions and that there exists an optimal level of phenotypic diversity best promoting contingent cooperation. It pays for contingent cooperators to elevate their potential of phenotypic variation, thereby increasing their opportunities of establishing cooperation via novel phenotypes, as these new phenotypes serve as secret tags that are difficult for defector to discover and chase after. We also find that evolved high levels of phenotypic diversity can occasionally collapse due to the invasion of defector mutants, suggesting that cooperation and phenotypic diversity can mutually reinforce each other. Thus, our results provide new insights into better understanding the coevolution of cooperation and phenotypic diversity.

Phenotypic variation is commonly observed from human cells to the intestinal pathogen Salmonella enterica serovar Typhimurium to the wrinkly-spreader morphs. Such phenotypic diversity proves effective in promoting cooperation, or confers survival advantage against unfavorable environmental changes. Prior studies show that interactions based on phenotypic similarity can promote cooperation. Yet in these models, the level of phenotypic diversity is prescribed such that individuals each possess the same number of available phenotypes, and thereby no evolution of phenotypic diversity per se. We here take into consideration important aspects of the diversity of phenotype and contingent cooperation and show that phenotypic diversity coevolves with cooperation under a variety of conditions. Our work provides a potential mechanism for the evolution of cooperation, and individuals, especially cooperators, endowed with diverse phenotypes constitute the backbone in inducing the coevolution.

Growth, collapse, and self-organized criticality in complex networks

Network growth is ubiquitous in nature (e.g., biological networks) and technological systems (e.g., modern infrastructures). To understand how certain dynamical behaviors can or cannot persist as the underlying network grows is a problem of increasing importance in complex dynamical systems as well as sustainability science and engineering. We address the question of whether a complex network of nonlinear oscillators can maintain its synchronization stability as it expands. We find that a large scale avalanche over the entire network can be triggered in the sense that the individual nodal dynamics diverges from the synchronous state in a cascading manner within a relatively short time period. In particular, after an initial stage of linear growth, the network typically evolves into a critical state where the addition of a single new node can cause a group of nodes to lose synchronization, leading to synchronization collapse for the entire network. A statistical analysis reveals that the collapse size is approximately algebraically distributed, indicating the emergence of self-organized criticality. We demonstrate the generality of the phenomenon of synchronization collapse using a variety of complex network models, and uncover the underlying dynamical mechanism through an eigenvector analysis.

Optimizing cooperation on complex networks in the presence of failure

Cooperation has been recognized as a fundamental driving force in many natural, social, and economic systems. We investigate whether, given a complex-networked system in which agents (nodes) interact with one another according to the rules of evolutionary games and are subject to failure or death, cooperation can prevail and be optimized. We articulate a control scheme to maximize cooperation by introducing a time tolerance, a time duration that sustains an agent even if its payoff falls below a threshold. Strikingly, we find that a significant cooperation cluster can emerge when the time tolerance is approximately uniformly distributed over the network. A heuristic theory is derived to understand the optimization mechanism, which emphasizes the role played by medium-degree nodes. Implications for policy making to prevent or mitigate large-scale cascading breakdown are pointed out.

Cascading failures and the emergence of cooperation in evolutionary-game based models of social and economical networks

We study catastrophic behaviors in large networked systems in the paradigm of evolutionary games by incorporating a realistic "death" or "bankruptcy" mechanism. We find that a cascading bankruptcy process can arise when defection strategies exist and individuals are vulnerable to deficit. Strikingly, we observe that, after the catastrophic cascading process terminates, cooperators are the sole survivors, regardless of the game types and of the connection patterns among individuals as determined by the topology of the underlying network. It is necessary that individuals cooperate with each other to survive the catastrophic failures. Cooperation thus becomes the optimal strategy and absolutely outperforms defection in the game evolution with respect to the "death" mechanism. Our results can be useful for understanding large-scale catastrophe in real-world systems and in particular, they may yield insights into significant social and economical phenomena such as large-scale failures of financial institutions and corporations during an economic recession.

Phase diagrams for the spatial public goods game with pool punishment

The efficiency of institutionalized punishment is studied by evaluating the stationary states in the spatial public goods game comprising unconditional defectors, cooperators, and cooperating pool punishers as the three competing strategies. Fines and costs of pool punishment are considered as the two main parameters determining the stationary distributions of strategies on the square lattice. Each player collects a payoff from five five-person public goods games, and the evolution of strategies is subsequently governed by imitation based on pairwise comparisons at a low level of noise. The impact of pool punishment on the evolution of cooperation in structured populations is significantly different from that reported previously for peer punishment. Representative phase diagrams reveal remarkably rich behavior, depending also on the value of the synergy factor that characterizes the efficiency of investments payed into the common pool. Besides traditional single- and two-strategy stationary states, a rock-paper-scissors type of cyclic dominance can emerge in strikingly different ways.

Feedback reciprocity mechanism promotes the cooperation of highly clustered scale-free networks

We study how the clustering coefficient influences the evolution of cooperation in scale-free public goods games. In games played by groups of individuals, triangle loops provide stronger support for mutual cooperation to resist invasion of selfish behavior than that in the absence of such loops, so that diffusion of cooperative behavior is relatively promoted. The feedback reciprocity mechanism of triangle plays a key role in facilitating cooperation in high clustered networks.