Noise-guided evolution within cyclical interactions

We study a stochastic predator-prey model on a square lattice, where each of the six species has two superior and two inferior partners. The invasion probabilities between species depend on the predator-prey pair and are supplemented by Gaussian noise. Conditions are identified that warrant the largest impact of noise on the evolutionary process, and the results of Monte Carlo simulations are qualitatively reproduced by a four-point cluster dynamical mean-field approximation. The observed noise-guided evolution is deeply routed in short-range spatial correlations, which is supported by simulations on other host lattice topologies. Our findings are conceptually related to the coherence resonance phenomenon in dynamical systems via the mechanism of threshold duality. We also show that the introduced concept of noise-guided evolution via the exploitation of threshold duality is not limited to predator-prey cyclical interactions, but may apply to models of evolutionary game theory as well, thus indicating its applicability in several different fields of research.Comment: to be published in New J. Phy

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

Mathematical foundations of moral preferences

One-shot anonymous unselfishness in economic games is commonly explained by social preferences, which assume that people care about the monetary payoffs of others. However, during the last ten years, research has shown that different types of unselfish behaviour, including cooperation, altruism, truth-telling, altruistic punishment, and trustworthiness are in fact better explained by preferences for following one’s own personal norms – internal standards about what is right or wrong in a given situation. Beyond better organ- ising various forms of unselfish behaviour, this moral preference hypothesis has recently also been used to increase charitable donations, simply by means of interventions that make the morality of an action salient. Here we review experimental and theoretical work dedicated to this rapidly growing field of research, and in doing so we outline mathematical foundations for moral preferences that can be used in future models to better understand selfless human actions and to adjust policies accordingly. These foundations can also be used by artificial intelligence to better navigate the complex landscape of human morality

Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games

Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the spatial dynamical rules are considered. The players following one of the two pure strategies (cooperation or defection) are distributed on a two-dimensional lattice. The rate of strategy adoption from a randomly chosen neighbors are controlled by the payoff difference and a two-value pre-factor $w$ characterizing the players whom the strategy learned from. The reduced teaching activity of players is distributed randomly with concentrations $\nu$ at the beginning and fixed further on. Numerical and analytical calculations are performed to study the concentration of cooperators as a function of $w$ and $\nu$ for different noise levels and connectivity structures. Significant increase of cooperation is found within a wide range of parameters for this dynamics. The results highlight the importance of asymmetry characterizing the exchange of master-follower role during the strategy adoptions.Comment: 4 pages, 5 figures, corrected typo

Evolutionary advantages of adaptive rewarding

Our wellbeing depends as much on our personal success, as it does on the success of our society. The realization of this fact makes cooperation a very much needed trait. Experiments have shown that rewards can elevate our readiness to cooperate, but since giving a reward inevitably entails paying a cost for it, the emergence and stability of such behavior remain elusive. Here we show that allowing for the act of rewarding to self-organize in dependence on the success of cooperation creates several evolutionary advantages that instill new ways through which collaborative efforts are promoted. Ranging from indirect territorial battle to the spontaneous emergence and destruction of coexistence, phase diagrams and the underlying spatial patterns reveal fascinatingly reach social dynamics that explains why this costly behavior has evolved and persevered. Comparisons with adaptive punishment, however, uncover an Achilles heel of adaptive rewarding that is due to over-aggression, which in turn hinders optimal utilization of network reciprocity. This may explain why, despite of its success, rewarding is not as firmly weaved into our societal organization as punishment.Comment: 14 pages, 8 figures; accepted for publication in New Journal of Physic

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

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

Excessive abundance of common resources deters social responsibility selection experiments teach us about fisheries-induced evolution?

We study the evolution of cooperation in the collective-risk social dilemma game, where the risk is determined by a collective target that must be reached with individual contributions. All players initially receive endowments from the available amount of common resources. While cooperators contribute part of their endowment to the collective target, defectors do not. If the target is not reached, the endowments of all players are lost. In our model, we introduce a feedback between the amount of common resources and the contributions of cooperators. We show that cooperation can be sustained only if the common resources are preserved but never excessively abound. This, however, requires a delicate balance between the amount of common resources that initially exist, and the amount cooperators contribute to the collective target. Exceeding critical thresholds in either of the two amounts leads to loss of cooperation, and consequently to the depletion of common resources

Information sharing promotes prosocial behaviour

More often than not, bad decisions are bad regardless of where and when they are made. Information sharing might thus be utilized to mitigate them. Here we show that sharing information about strategy choice between players residing on two different networks reinforces the evolution of cooperation. In evolutionary games, the strategy reflects the action of each individual that warrants the highest utility in a competitive setting. We therefore assume that identical strategies on the two networks reinforce themselves by lessening their propensity to change. Besides network reciprocity working in favour of cooperation on each individual network, we observe the spontaneous emergence of correlated behaviour between the two networks, which further deters defection. If information is shared not just between individuals but also between groups, the positive effect is even stronger, and this despite the fact that information sharing is implemented without any assumptions with regard to content