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

Self-organizing patterns maintained by competing associations in a six-species predator-prey model

Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The evolution of the spatial distribution of species is governed by iterated invasions between the neighboring predator-prey pairs with species specific rates and by site exchange between the neutral pairs with a probability $X$. This dynamical rule yields the formation of five associations composed of two or three species with proper spatiotemporal patterns. For large $X$ a cyclic dominance can occur between the three two-species associations whereas one of the two three-species associations prevails in the whole system for low values of $X$ in the final state. Within an intermediate range of $X$ all the five associations coexist due to the fact that cyclic invasions between the two-species associations reduce their resistance temporarily against the invasion of three-species associations.Comment: 6 pages, 8 figure

Sustainable institutionalized punishment requires elimination of second-order free-riders

Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the "punishment pool" from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.Comment: 7 two-column pages, 3 figures; accepted for publication in Scientific Report

If cooperation is likely punish mildly: Insights from economic experiments based on the snowdrift game

Punishment may deter antisocial behavior. Yet to punish is costly, and the costs often do not offset the gains that are due to elevated levels of cooperation. However, the effectiveness of punishment depends not only on how costly it is, but also on the circumstances defining the social dilemma. Using the snowdrift game as the basis, we have conducted a series of economic experiments to determine whether severe punishment is more effective than mild punishment. We have observed that severe punishment is not necessarily more effective, even if the cost of punishment is identical in both cases. The benefits of severe punishment become evident only under extremely adverse conditions, when to cooperate is highly improbable in the absence of sanctions. If cooperation is likely, mild punishment is not less effective and leads to higher average payoffs, and is thus the much preferred alternative. Presented results suggest that the positive effects of punishment stem not only from imposed fines, but may also have a psychological background. Small fines can do wonders in motivating us to chose cooperation over defection, but without the paralyzing effect that may be brought about by large fines. The later should be utilized only when absolutely necessary.Comment: 15 pages, 6 figures; accepted for publication in PLoS ON

Optimal distribution of phosphorus compounds in multi-layered natural fabric reinforced biocomposites

Flame retardancy and mechanical performance of multi-layered biocomposites, consisting of polylactic acid (PLA) matrix films and plain-woven flax fabrics as reinforcement, were investigated. Full factorial design (32) was applied to evaluate the effects of the distribution of P and N containing compounds between the matrix and the fibrous carrier. Composition property correlations of the composite constituents (i.e. flax fabrics treated in aqueous solutions of diammonium phosphate and urea with differing ratio and concentrations and matrix films with 0 to 20 wt% ammonium polyphosphate based intumescent flame retardant content) were determined by thermogravimetric analyses and open flame tests. Positive interaction between the composite constituents was revealed for green composites consisting of various combinations of treated fabrics and intumescent PLA systems. The biocomposites flame retarded with a combined approach, i.e. with a balanced distribution of P containing additives between the phases, were found to gain improved mechanical performance and fire retardancy. It was confirmed by tensile testing and electron microscopy as well as by UL-94, limiting oxygen index and cone calorimeter tests. As a conclusion, interpretation is given for the optimum found

Patterns of cooperation: fairness and coordination in networks of interacting agents

We study the self-assembly of a complex network of collaborations among self-interested agents. The agents can maintain different levels of cooperation with different partners. Further, they continuously, selectively, and independently adapt the amount of resources allocated to each of their collaborations in order to maximize the obtained payoff. We show analytically that the system approaches a state in which the agents make identical investments, and links produce identical benefits. Despite this high degree of social coordination some agents manage to secure privileged topological positions in the network enabling them to extract high payoffs. Our analytical investigations provide a rationale for the emergence of unidirectional non-reciprocal collaborations and different responses to the withdrawal of a partner from an interaction that have been reported in the psychological literature.Comment: 20 pages, 8 figure

Resolution of the stochastic strategy spatial prisoner's dilemma by means of particle swarm optimization

We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoner's dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoner's dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.Comment: 12 pages, 4 figures; accepted for publication in PLoS ON

Special Agents Can Promote Cooperation in the Population

Cooperation is ubiquitous in our real life but everyone would like to maximize her own profits. How does cooperation occur in the group of self-interested agents without centralized control? Furthermore, in a hostile scenario, for example, cooperation is unlikely to emerge. Is there any mechanism to promote cooperation if populations are given and play rules are not allowed to change? In this paper, numerical experiments show that complete population interaction is unfriendly to cooperation in the finite but end-unknown Repeated Prisoner's Dilemma (RPD). Then a mechanism called soft control is proposed to promote cooperation. According to the basic idea of soft control, a number of special agents are introduced to intervene in the evolution of cooperation. They comply with play rules in the original group so that they are always treated as normal agents. For our purpose, these special agents have their own strategies and share knowledge. The capability of the mechanism is studied under different settings. We find that soft control can promote cooperation and is robust to noise. Meanwhile simulation results demonstrate the applicability of the mechanism in other scenarios. Besides, the analytical proof also illustrates the effectiveness of soft control and validates simulation results. As a way of intervention in collective behaviors, soft control provides a possible direction for the study of reciprocal behaviors

Motion of influential players can support cooperation in Prisoner's Dilemma

We study a spatial Prisoner's dilemma game with two types (A and B) of players located on a square lattice. Players following either cooperator or defector strategies play Prisoner's Dilemma games with their 24 nearest neighbors. The players are allowed to adopt one of their neighbor's strategy with a probability dependent on the payoff difference and type of the given neighbor. Players A and B have different efficiency in the transfer of their own strategy therefore the strategy adoption probability is reduced by a multiplicative factor (w < 1) from the players of type B. We report that the motion of the influential payers (type A) can improve remarkably the maintenance of cooperation even for their low densities.Comment: 7 pages, 7 figure

Fixation times in evolutionary games under weak selection

In evolutionary game dynamics, reproductive success increases with the performance in an evolutionary game. If strategy $A$ performs better than strategy $B$, strategy $A$ will spread in the population. Under stochastic dynamics, a single mutant will sooner or later take over the entire population or go extinct. We analyze the mean exit times (or average fixation times) associated with this process. We show analytically that these times depend on the payoff matrix of the game in an amazingly simple way under weak selection, ie strong stochasticity: The payoff difference $\Delta \pi$ is a linear function of the number of $A$ individuals $i$, $\Delta \pi = u i + v$. The unconditional mean exit time depends only on the constant term $v$. Given that a single $A$ mutant takes over the population, the corresponding conditional mean exit time depends only on the density dependent term $u$. We demonstrate this finding for two commonly applied microscopic evolutionary processes.Comment: Forthcoming in New Journal of Physic