Making new connections towards cooperation in the prisoner's dilemma game

Evolution of cooperation in the prisoner's dilemma game is studied where initially all players are linked via a regular graph, having four neighbors each. Simultaneously with the strategy evolution, players are allowed to make new connections and thus permanently extend their neighborhoods, provided they have been successful in passing their strategy to the opponents. We show that this simple coevolutionary rule shifts the survival barrier of cooperators towards high temptations to defect and results in highly heterogeneous interaction networks with an exponential fit best characterizing their degree distributions. In particular, there exist an optimal maximal degree for the promotion of cooperation, warranting the best exchange of information between influential players.Comment: 6 two-column pages, 7 figures; accepted for publication in Europhysics Letter

Selection of dynamical rules in spatial Prisoner's Dilemma games

We study co-evolutionary Prisoner's Dilemma games where each player can imitate both the strategy and imitation rule from a randomly chosen neighbor with a probability dependent on the payoff difference when the player's income is collected from games with the neighbors. The players, located on the sites of a two-dimensional lattice, follow unconditional cooperation or defection and use individual strategy adoption rule described by a parameter. If the system is started from a random initial state then the present co-evolutionary rule drives the system towards a state where only one evolutionary rule remains alive even in the coexistence of cooperative and defective behaviors. The final rule is related to the optimum providing the highest level of cooperation and affected by the topology of the connectivity structure.Comment: 5 two-column pages, 3 figure

Evolutionary dynamics of cooperation in neutral populations

Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the formation of homogeneous clusters, which is the hallmark of network reciprocity. Here we go beyond this traditional setup and study the spatiotemporal dynamics of cooperation in a population of populations. We use the prisoner's dilemma game as the mathematical model and show that considering several populations simultaneously give rise to fascinating spatiotemporal dynamics and pattern formation. Even the simplest assumption that strategies between different populations are payoff-neutral with one another results in the spontaneous emergence of cyclic dominance, where defectors of one population become prey of cooperators in the other population, and vice versa. Moreover, if social interactions within different populations are characterized by significantly different temptations to defect, we observe that defectors in the population with the largest temptation counterintuitively vanish the fastest, while cooperators that hang on eventually take over the whole available space. Our results reveal that considering the simultaneous presence of different populations significantly expands the complexity of evolutionary dynamics in structured populations, and it allow us to understand the stability of cooperation under adverse conditions that could never be bridged by network reciprocity alone.Comment: 14 pages, 7 figures; accepted for publication in New Journal of Physic

Restricted connections among distinguished players support cooperation

We study the evolution of cooperation within the spatial prisoner's dilemma game on a square lattice where a fraction of players $\mu$ can spread their strategy more easily than the rest due to a predetermined larger teaching capability. In addition, players characterized with the larger teaching capability are allowed to temporarily link with distant opponents of the same kind with probability $p$, thus introducing shortcut connections among the distinguished. We show that these additional temporary connections are able to sustain cooperation throughout the whole range of the temptation to defect. Remarkably, we observe that as the temptation to defect increases the optimal $\mu$ decreases, and moreover, only minute values of $p$ warrant the best promotion of cooperation. Our study thus indicates that influential individuals must be few and sparsely connected in order for cooperation to thrive in a defection prone environment.Comment: 6 two-column pages, 6 figures; accepted for publication in Physical Review

Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system

Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly new situation emerges if we introduce an apex predator who can superior all members of the mentioned three-species system. In the latter case the evolution may terminate into three qualitatively different destinations depending on the apex predator decaying ratio $q$. In particular, the whole population goes extinct or all four species survive or only the original three-species system remains alive as we vary the control parameter. These solutions are separated by a discontinuous and a continuous phase transitions at critical $q$ values. Our results highlight that cyclic dominant competition can offer a stable way to survive even in a predator-prey-like system that can be maintained for large interval of critical parameter values.Comment: version to appear in EPL. 7 pages, 7 figure

Invasion controlled pattern formation in a generalized multi-species predator-prey system

Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier.Comment: 8 pages, 8 figures. To appear in PR

Self-organization of punishment in structured populations

Cooperation is crucial for the remarkable evolutionary success of the human species. Not surprisingly, some individuals are willing to bare additional costs in order to punish defectors. Current models assume that, once set, the fine and cost of punishment do not change over time. Here we show that relaxing this assumption by allowing players to adapt their sanctioning efforts in dependence on the success of cooperation can explain both, the spontaneous emergence of punishment, as well as its ability to deter defectors and those unwilling to punish them with globally negligible investments. By means of phase diagrams and the analysis of emerging spatial patterns, we demonstrate that adaptive punishment promotes public cooperation either through the invigoration of spatial reciprocity, the prevention of the emergence of cyclic dominance, or through the provision of competitive advantages to those that sanction antisocial behavior. Presented results indicate that the process of self-organization significantly elevates the effectiveness of punishment, and they reveal new mechanisms by means of which this fascinating and widespread social behavior could have evolved.Comment: 13 pages, 4 figures; accepted for publication in New Journal of Physic

Interdependent network reciprocity in evolutionary games

Besides the structure of interactions within networks, also the interactions between networks are of the outmost importance. We therefore study the outcome of the public goods game on two interdependent networks that are connected by means of a utility function, which determines how payoffs on both networks jointly influence the success of players in each individual network. We show that an unbiased coupling allows the spontaneous emergence of interdependent network reciprocity, which is capable to maintain healthy levels of public cooperation even in extremely adverse conditions. The mechanism, however, requires simultaneous formation of correlated cooperator clusters on both networks. If this does not emerge or if the coordination process is disturbed, network reciprocity fails, resulting in the total collapse of cooperation. Network interdependence can thus be exploited effectively to promote cooperation past the limits imposed by isolated networks, but only if the coordination between the interdependent networks is not disturbe

Self-organization towards optimally interdependent networks by means of coevolution

Coevolution between strategy and network structure is established as a means to arrive at the optimal conditions needed to resolve social dilemmas. Yet recent research has highlighted that the interdependence between networks may be just as important as the structure of an individual network. We therefore introduce the coevolution of strategy and network interdependence to see whether this can give rise to elevated levels of cooperation in the prisonerʼs dilemma game. We show that the interdependence between networks self-organizes so as to yield optimal conditions for the evolution of cooperation. Even under extremely adverse conditions, cooperators can prevail where on isolated networks they would perish. This is due to the spontaneous emergence of a two-class society, with only the upper class being allowed to control and take advantage of the interdependence. Spatial patterns reveal that cooperators, once arriving at the upper class, are much more competent than defectors in sustaining compact clusters of followers. Indeed, the asymmetric exploitation of interdependence confers to them a strong evolutionary advantage that may resolve even the toughest of social dilemmas

Topological enslavement in evolutionary games on correlated multiplex networks

Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoner's dilemma or the harmony game, with imitation dynamics. Adjusting the incentives by changing the payoff parameters can favor cooperation, as found in the harmony game, over defection, which prevails in the prisoner's dilemma. Here, we show that this is not always the case if individuals engage in strategic interactions in multiple domains. In particular, we investigate evolutionary games on multiplex networks where individuals obtain an aggregate payoff. We explicitly control the strength of degree correlations between nodes in the different layers of the multiplex. We find that if the multiplex is composed of many layers and degree correlations are strong, the topology of the system enslaves the dynamics and the final outcome, cooperation or defection, becomes independent of the payoff parameters. The fate of the system is then determined by the initial conditions