The effects of an unconditional move rule in the spatial Prisoner's Dilemma, Snowdrift and Stag Hunt games are studied. Spatial structure by itself is known to modify the outcome of many games when compared with a randomly mixed population, sometimes promoting, sometimes inhibiting cooperation. Here we show that random dilution and mobility may suppress the inhibiting factors of the spatial structure in the Snowdrift game, while enhancing the already larger cooperation found in the Prisoner's dilemma and Stag Hunt games.
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters they might share the benefit of cooperation while being more protected against non-cooperating individuals, which benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups fitness collection and selection are separated processes occurring mostly on vastly different time scales. Th…
We explore the minimal conditions for sustainable cooperation on a spatially distributed population of memoryless, unconditional strategies (cooperators and defectors) in presence of unbiased, non contingent mobility in the context of the Prisoner's Dilemma game. We find that cooperative behavior is not only possible but may even be enhanced by such an ``always-move'' rule, when compared with the strongly viscous (``never-move'') case. In addition, mobility also increases the capability of cooperation to emerge and invade a population of defectors, what may have a fundamental role in the probl…
Cooperation among individuals has been key to sustaining societies. However, natural selection favors defection over cooperation. Cooperation can be favored when the mobility of individuals allows cooperators to form a cluster (or group). Mobility patterns of animals sometimes follow a Lévy flight. A Lévy flight is a kind of random walk but it is composed of many small movements with a few big movements. The role of Lévy flights for cooperation has been studied by Antonioni and Tomassini. They showed that Lévy flights promoted cooperation combined with conditional movements triggered by neighb…
We investigate the effect of randomness in both relationships and decisions on the evolution of cooperation. Simulation results show, in such randomness' presence, the system evolves to a more frequency cooperation state than in its absence. Specifically, there is an optimal amount of randomness, which can induce the highest level of cooperation. The mechanism of randomness promoting cooperation resembles a coherence-resonance-like fashion, which could be of particular interest in evolutionary game dynamics in economic, biological and social systems.
We study the effect of contingent movement on the persistence of cooperation on complex networks with empty nodes. Each agent plays Prisoner's Dilemma game with its neighbors and then it either updates the strategy depending on the payoff difference with neighbors or it moves to another empty node if not satisfied with its own payoff. If no neighboring node is empty, each agent stays at the same site. By extensive evolutionary simulations, we show that the medium density of agents enhances cooperation where the network flow of mobile agents is also medium. Moreover, if the movements of agents …
Social hierarchy is important that can not be ignored in human socioeconomic activities and in the animal world. Here we incorporate this factor into the evolutionary game to see what impact it could have on the cooperation outcome. The probabilistic strategy adoption between two players is then not only determined by their payoffs, but also by their hierarchy difference -- players in the high rank are more likely to reproduce their strategies than the peers in the low rank. Through simulating the evolution of Prisoners' dilemma game with three hierarchical distributions, we find that the leve…
The promotion of cooperation on spatial lattices is an important issue in evolutionary game theory. This effect clearly depends on the update rule: it diminishes with stochastic imitative rules whereas it increases with unconditional imitation. To study the transition between both regimes, we propose a new evolutionary rule, which stochastically combines unconditional imitation with another imitative rule. We find that, surprinsingly, in many social dilemmas this rule yields higher cooperative levels than any of the two original ones. This nontrivial effect occurs because the basic rules induc…
In multi-agent systems, cooperative behavior is largely determined by the network structure which dictates the interactions among neighboring agents. These interactions often exhibit multidimensional features, either as relationships of different types or temporal dynamics, both of which may be modeled as a "multiplex" network. Against this background, here we advance the research on cooperation models inspired by generalized reciprocity, a simple pay-it-forward behavioral mechanism, by considering a multidimensional networked society. Our results reveal that a multiplex network structure can …
Synergies between evolutionary game theory and statistical physics have significantly improved our understanding of public cooperation in structured populations. Multiplex networks, in particular, provide the theoretical framework within network science that allows us to mathematically describe the rich structure of interactions characterizing human societies. While research has shown that multiplex networks may enhance the resilience of cooperation, the interplay between the overlap in the structure of the layers and the control parameters of the corresponding games has not yet been investiga…
Cooperation is ubiquitous in biological and social systems. Previous studies revealed that a preference toward similar appearance promotes cooperation, a phenomenon called tag-mediated cooperation or communitarian cooperation. This effect is enhanced when a spatial structure is incorporated, because space allows agents sharing an identical tag to regroup to form locally cooperative clusters. In spatially distributed settings, one can also consider migration of organisms, which has a potential to further promote evolution of cooperation by facilitating spatial clustering. However, it has not ye…
Game theory research on the snowdrift game has showed that gradual evolution of the continuously varying level of cooperation in joint enterprises can demonstrate evolutionary merging as well as evolutionary branching. However, little is known about the consequences of changes in diversity at the cooperation level. In the present study I consider effects of costly rewards on the continuous snowdrift game. I show that not evolutionary merging but evolutionary branching can promote the emergence of pool reward, which can then enhance social welfare.
Recent research has identified the heterogeneity as crucial for the evolution of cooperation in spatial population. However, the influence of heterogeneous noise is still lack. Inspired by this interesting question, in this work, we try to incorporate heterogeneous noise into the evaluation of utility, where only a proportion of population possesses noise, whose range can also be tuned. We find that increasing heterogeneous noise monotonously promotes cooperation and even translates the full defection phase (of the homogeneous version) into the complete cooperation phase. Moreover, the promoti…
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 $ν$ at the beginning and fixed further on. Numerical and analytical calculations …
In the framework of the paradigmatic prisoner's dilemma, we investigate the evolutionary dynamics of social dilemmas in the presence of "cooperation facilitators". In our model, cooperators and defectors interact as in the classical prisoner's dilemma game, where selection favors defection. However, here the presence of a small number of cooperation facilitators enhances the fitness (reproductive potential) of cooperators, while it does not alter that of defectors. In a finite population of size N, the dynamics of the prisoner's dilemma with facilitators is characterized by the probability tha…
Recent studies on the evolutionary dynamics of the Prisoner's Dilemma game in scale-free networks have demonstrated that the heterogeneity of the network interconnections enhances the evolutionary success of cooperation. In this paper we address the issue of how the characterization of the asymptotic states of the evolutionary dynamics depends on the initial concentration of cooperators. We find that the measure and the connectedness properties of the set of nodes where cooperation reaches fixation is largely independent of initial conditions, in contrast with the behavior of both the set of n…
Aging is always present, tailoring our interactions with others and postulating a finite lifespan during which we are able to exercise them. We consider the prisoner's dilemma game on a square lattice, and examine how quenched age distributions and different aging protocols influence the evolution of cooperation when taking the life experience and knowledge accumulation into account as time passes. In agreement with previous studies, we find that a quenched assignment of age to players, introducing heterogeneity to the game, substantially promotes cooperative behavior. Introduction of aging an…
Prevalence of cooperation within groups of selfish individuals is puzzling in that it contradicts with the basic premise of natural selection. Favoring players with higher fitness, the latter is key for understanding the challenges faced by cooperators when competing with defectors. Evolutionary game theory provides a competent theoretical framework for addressing the subtleties of cooperation in such situations, which are known as social dilemmas. Recent advances point towards the fact that the evolution of strategies alone may be insufficient to fully exploit the benefits offered by cooperat…
We study the evolution of cooperation in public goods games on the square lattice, focusing on the effects that are brought about by different sizes of groups where individuals collect their payoffs and search for potential strategy donors. We find that increasing the group size does not necessarily lead to mean-field behavior, as is traditionally observed for games governed by pairwise interactions, but rather that public cooperation may be additionally promoted by means of enhanced spatial reciprocity that sets in for very large groups. Our results highlight that the promotion of cooperation…
Recent studies suggest that the emergence of cooperative behavior can be explained by generalized reciprocity, a behavioral mechanism based on the principle of "help anyone if helped by someone". In complex systems, the cooperative dynamics is largely determined by the network structure which dictates the interactions among neighboring individuals. These interactions often exhibit multidimensional features, either as relationships of different types or temporal dynamics, both of which may be modeled as a "multiplex" network. Against this background, here we advance the research on cooperation …
Population structure and spatial heterogeneity are integral components of evolutionary dynamics, in general, and of evolution of cooperation, in particular. Structure can promote the emergence of cooperation in some populations and suppress it in others. Here, we provide results for weak selection to favor cooperation on regular graphs for any configuration, meaning any arrangement of cooperators and defectors. Our results extend previous work on fixation probabilities of single, randomly placed mutants. We find that for any configuration cooperation is never favored for birth-death (BD) updat…
King Fahd University of Petroleum and Minerals（国王法赫德国王石油与矿产大学）；University of Montreal（蒙特利尔大学）
We consider interactions between players in groups of size $d\geq2$ with payoffs that not only depend on the strategies used in the group but also fluctuate at random over time. An individual can adopt either cooperation or defection as strategy and the population is updated from one-time step to the next by a birth-death event according to a Moran model. Assuming recurrent symmetric mutation and payoffs with expected values, variances, and covariances of the same small order, we derive a first-order approximation of the average abundance of cooperation in the selection-mutation equilibrium. W…
We present a novel approach allowing the study of rare events like fixation under fluctuating environments, modeled as extrinsic noise, in evolutionary processes characterized by the dominance of one species. Our treatment consists of mapping the system onto an auxiliary model, exhibiting metastable species coexistence, that can be analyzed semiclassically. This approach enables us to study the interplay between extrinsic and demographic noise on the statistics of interest. We illustrate our theory by considering the paradigmatic prisoner's dilemma game whose evolution is described by the prob…
