Spatial Patterns of Prisoner’s Dilemma Game in Metapopulations

Because to defect is the evolutionary stable strategy in the prisoner’s dilemma game (PDG), understanding the mechanism generating and maintaining cooperation in PDG, i.e. the paradox of cooperation, has intrinsic significance for understanding social altruism behaviors. Spatial structure serves as the key to this dilemma. Here, we build the model of spatial PDG under a metapopulation framework: the sub-populations of cooperators and defectors obey the rules in spatial PDG as well as the colonization–extinction process of metapopulations. Using the mean-field approximation and the pair approximation, we obtain the differential equations for the dynamics of occupancy and spatial correlation. Cellular automaton is also built to simulate the spatiotemporal dynamics of the spatial PDG in metapopulations. Join-count statistics are used to measure the spatial correlation as well as the spatial association of the metapopulation. Simulation results show that the distribution is self-organized and that it converges to a static boundary due to the boycotting of cooperators to defectors. Metapopulations can survive even when the colonization rate is lower than the extinction rate due to the compensation of cooperation rewards for extinction debt. With a change of parameters in the model, a metapopulation can consist of pure cooperators, pure defectors, or cooperator–defector coexistence. The necessary condition of cooperation evolution is the local colonization of a metapopulation. The spatial correlation between the cooperators tends to be weaker with the increase in the temptation to defect and the habitat connectivity; yet the spatial correlation between defectors becomes stronger. The relationship between spatial structure and the colonization rate is complicated, especially for cooperators. The metapopulation may undergo a temporary period of prosperity just before the extinction, even while the colonization rate is declining. An erratum to this article can be found at     

Heterogeneous Coupling between Interdependent Lattices Promotes the Cooperation in the Prisoner’s Dilemma Game

In the research realm of game theory, interdependent networks have extended the content of spatial reciprocity, which needs the suitable coupling between networks. However, thus far, the vast majority of existing works just assume that the coupling strength between networks is symmetric. This hypothesis, to some extent, seems inconsistent with the ubiquitous observation of heterogeneity. Here, we study how the heterogeneous coupling strength, which characterizes the interdependency of utility between corresponding players of both networks, affects the evolution of cooperation in the prisoner’s dilemma game with two types of coupling schemes (symmetric and asymmetric ones). Compared with the traditional case, we show that heterogeneous coupling greatly promotes the collective cooperation. The symmetric scheme seems much better than the asymmetric case. Moreover, the role of varying amplitude of coupling strength is also studied on these two interdependent ways. Current findings are helpful for us to understand the evolution of cooperation within many real-world systems, in particular for the interconnected and interrelated systems.     

Lack of Association between Human Plasma Oxytocin and Interpersonal Trust in a Prisoner’s Dilemma Paradigm

Expanding interest in oxytocin, particularly the role of endogenous oxytocin in human social behavior, has created a pressing need for replication of results and verification of assay methods. In this study, we sought to replicate and extend previous results correlating plasma oxytocin with trust and trustworthy behavior. As a necessary first step, the two most commonly used commercial assays were compared in human plasma via the addition of a known quantity of exogenous oxytocin, with and without sample extraction. Plasma sample extraction was found to be critical in obtaining repeatable concentrations of oxytocin. In the subsequent trust experiment, twelve samples in duplicate, from each of 82 participants, were collected over approximately six hours during the performance of a Prisoner’s Dilemma task paradigm that stressed human interpersonal trust. We found no significant relationship between plasma oxytocin concentrations and trusting or trustworthy behavior. In light of these findings, previous published work that used oxytocin immunoassays without sample extraction should be reexamined and future research exploring links between endogenous human oxytocin and trust or social behavior should proceed with careful consideration of methods and appropriate biofluids for analysis.     

Relational Diversity Promotes Cooperation in Prisoner’s Dilemma Games

Relational diversity can be characterized by heterogeneous distributions of tie strengths in social networks and this diversity is present not only among humans, but throughout the animal world. We account for this observation by analyzing two network datasets from Facebook. We measure the strength of a tie by calculating the extent of overlap of friends between the two individuals. Based on the previous findings in human experiments, we argue that it is very unlikely that players will allocate their investments equally to their neighbors. There is a tendency that players prefer to donate more to their intimate friends. We find that if players preferentially allocate their investments to their good friends, cooperation will be promoted in PDG. We proved that the facilitation of the cooperative strategy relies mostly on the cooperative allies between best friends, resulting in the formation of cooperative clusters which are able to prevail against the defectors even when there is a large cost to cooperate. Moreover, we discover that the effect of relational diversity cannot be analyzed by adopting classical complex networks models, because neither of the artificial networks is able to produce networks with diverse distributions of tie strengths. It is of vital importance to introduce real social networks to study the influence of diverse relations especially when it comes to humans. This research proposes a brand new perspective to understand the influence of social relations on the emergence of cooperation in evolutionary prisoner’s dilemma games.     

Dependency Links Can Hinder the Evolution of Cooperation in the Prisoner’s Dilemma Game on Lattices and Networks

Networks with dependency links are more vulnerable when facing the attacks. Recent research also has demonstrated that the interdependent groups support the spreading of cooperation. We study the prisoner’s dilemma games on spatial networks with dependency links, in which a fraction of individual pairs is selected to depend on each other. The dependency individuals can gain an extra payoff whose value is between the payoff of mutual cooperation and the value of temptation to defect. Thus, this mechanism reflects that the dependency relation is stronger than the relation of ordinary mutual cooperation, but it is not large enough to cause the defection of the dependency pair. We show that the dependence of individuals hinders, promotes and never affects the cooperation on regular ring networks, square lattice, random and scale-free networks, respectively. The results for the square lattice and regular ring networks are demonstrated by the pair approximation.     

Chasing genes in Alzheimer’s and Parkinson’s disease

Alzheimers disease (AD), the most common type of dementia, and Parkinsons disease (PD), the most common movement disorder, are both neurodegenerative adult-onset diseases characterized by the progressive loss of specific neuronal populations and the accumulation of intraneuronal inclusions. The search for genetic and environmental factors that determine the fate of neurons during the ageing process has been a widespread approach in the battle against neurodegenerative disorders. Genetic studies of AD and PD initially focused on the search for genes involved in the aetiological mechanisms of monogenic forms of these diseases. They later expanded to study hundreds of patients, affected relative-pairs and population-based studies, sometimes performed on special isolated populations. A growing number of genes (and pathogenic mutations) is being identified that cause or increase susceptibility to AD and PD. This review discusses the way in which strategies of gene hunting have evolved during the last few years and the significance of finding genes such as the presenilins, -synuclein, parkin and DJ-1. In addition, we discuss possible links between these two neurodegenerative disorders. The clinical, pathological and genetic presentation of AD and PD suggests the involvement of a few overlapping interrelated pathways. Their imbricate features point to a spectrum of neurodegeneration (tauopathies, synucleinopathies, amyloidopathies) that need further intense investigation to find the missing links.     

The Effect of Power Asymmetries on Cooperation and Punishment in a Prisoner’s Dilemma Game

Recent work has suggested that punishment is detrimental because punishment provokes retaliation, not cooperation, resulting in lower overall payoffs. These findings may stem from the unrealistic assumption that all players are equal: in reality individuals are expected to vary in the power with which they can punish defectors. Here, we allowed strong players to interact with weak players in an iterated prisoner''s dilemma game with punishment. Defecting players were most likely to switch to cooperation if the partner cooperated: adding punishment yielded no additional benefit and, under some circumstances, increased the chance that the partner would both defect and retaliate against the punisher. Our findings show that, in a two-player game, cooperation begets cooperation and that punishment does not seem to yield any additional benefits. Further work should explore whether strong punishers might prevail in multi-player games.     

Cooperation and Competition Between Twins: Findings from a Prisoner’s Dilemma Game

Attention to factors influencing cooperation and competition during human social interaction has increased within recent years. This study tested the hypothesis that higher levels of cooperation would be associated with increased genetic relatedness between interactants, and explored questions concerning the expression of cooperative behavior over time. A Prisoner’s Dilemma game, in which participants elect to display cooperative, competitive, or exploitative behaviors relative to a partner, was administered to 59 monozygotic and 37 dizygotic twin pairs, between 10.92 and 82.67 years of age. Results from multivariate analysis of variance procedures, cross-lag sequential analyses, and hierarchical linear modeling supported associations between zygosity, and frequency and continuity of cooperation. Mechanisms by which zygosity may affect cooperation were explored by examining relationships between response combinations, and twins’ IQ similarity and social closeness. The findings are considered with reference to an evolutionary perspective on behavior that offers a theoretical basis for considering how the relative genetic relatedness of social partners affects their social-interactional processes and outcomes. This report is the first in a series of studies designed to address mechanisms underlying differences in cooperation among pairs who vary in average genetic commonality.     

Modelling the Effects of Selection Temperature and Mutation on the Prisoner’s Dilemma Game on a Complete Oriented Star

This paper models the prisoner’s dilemma game based on pairwise comparison in finite populations on a complete oriented star (COS). First, we derive a linear system on a COS for calculating the corresponding fixation probabilities that imply dependence of the selection temperature and mutation. Then we observe and analyze the effects of two parameters on fixation probability under different population sizes. In particular, it is found through the experimental results that (1) high mutation is more sensitive to the fixation probability than the low one when population size is increasing, while the opposite is the case when the number of cooperators is increasing, and (2) selection temperature demotes the fixation probability.     

Emergence of Super Cooperation of Prisoner’s Dilemma Games on Scale-Free Networks

Recently, the authors proposed a quantum prisoner’s dilemma game based on the spatial game of Nowak and May, and showed that the game can be played classically. By using this idea, we proposed three generalized prisoner’s dilemma (GPD, for short) games based on the weak Prisoner’s dilemma game, the full prisoner’s dilemma game and the normalized Prisoner’s dilemma game, written by GPD_W, GPD_F and GPD_N respectively. Our games consist of two players, each of which has three strategies: cooperator (C), defector (D) and super cooperator (denoted by Q), and have a parameter γ to measure the entangled relationship between the two players. We found that our generalised prisoner’s dilemma games have new Nash equilibrium principles, that entanglement is the principle of emergence and convergence (i.e., guaranteed emergence) of super cooperation in evolutions of our generalised prisoner’s dilemma games on scale-free networks, that entanglement provides a threshold for a phase transition of super cooperation in evolutions of our generalised prisoner’s dilemma games on scale-free networks, that the role of heterogeneity of the scale-free networks in cooperations and super cooperations is very limited, and that well-defined structures of scale-free networks allow coexistence of cooperators and super cooperators in the evolutions of the weak version of our generalised prisoner’s dilemma games.     

Interaction characteristics as evolutionary features for the spatial Prisoner’s Dilemma in a population modeled by continuous probabilistic cellular automata and evolutionary algorithm

Evolutionary games usually take into consideration individuals’ strategies as the transformative characteristic which leads to the evolution of the population. Here, besides the strategies, interaction aspects are also considered as evolutionary attributes which can change over time as the replacement dynamic renovates the population choosing locally better individuals to reproduce. The population is modeled by cellular automata, interactions by the Prisoner’s Dilemma game and the replacement process is ruled by two versions of death-birth dynamic. Although the average payoff per game is considered as the fitness for choosing better individuals, the number of games per time step and a maximum radius of interaction with neighbours are also present in the individual’s chromosome which is passed to the next generation. Numerical simulations show that individual interaction properties and cooperation level are linked to the version of death-birth dynamic used and the game payoff. For instance, when the fitness bias is on the death event, individuals have more interactions in a larger radius, and the cooperation level is usually lower than the case where the fitness bias is on the birth event. Also, the individuals’ interaction profiles are heterogeneous, and cooperative individuals form clusters in the lattice to protect themselves.     

Regional Contingencies in the Relationship between Aboveground Biomass and Litter in the World’s Grasslands

Based on regional-scale studies, aboveground production and litter decomposition are thought to positively covary, because they are driven by shared biotic and climatic factors. Until now we have been unable to test whether production and decomposition are generally coupled across climatically dissimilar regions, because we lacked replicated data collected within a single vegetation type across multiple regions, obfuscating the drivers and generality of the association between production and decomposition. Furthermore, our understanding of the relationships between production and decomposition rests heavily on separate meta-analyses of each response, because no studies have simultaneously measured production and the accumulation or decomposition of litter using consistent methods at globally relevant scales. Here, we use a multi-country grassland dataset collected using a standardized protocol to show that live plant biomass (an estimate of aboveground net primary production) and litter disappearance (represented by mass loss of aboveground litter) do not strongly covary. Live biomass and litter disappearance varied at different spatial scales. There was substantial variation in live biomass among continents, sites and plots whereas among continent differences accounted for most of the variation in litter disappearance rates. Although there were strong associations among aboveground biomass, litter disappearance and climatic factors in some regions (e.g. U.S. Great Plains), these relationships were inconsistent within and among the regions represented by this study. These results highlight the importance of replication among regions and continents when characterizing the correlations between ecosystem processes and interpreting their global-scale implications for carbon flux. We must exercise caution in parameterizing litter decomposition and aboveground production in future regional and global carbon models as their relationship is complex.     

The Study of Cognitive Characteristics in Asperger’s Disorder by Using a Modified Prisoner’s Dilemma Game with a Variable Payoff Matrix

Individuals with Asperger’s Disorder (ASP) have difficulties in social reciprocity and in providing appropriate cooperative behavior. The Prisoner’s Dilemma (PD) is a well-known model in game theory that illustrates the paradoxical disposition of interaction between two individuals with opposing interests, and may be a useful tool in the diagnosis of ASP in early childhood. In this study, we investigated the cognitive characteristics of ASP by using a modified PD game. The subjects were 29 individuals with ASP and 28 age- and IQ-matched controls. In the PD game, each of two players has two cards: card 1 represents cooperation and card 2 betrayal. The score each player obtains is decided according to a 2 x 2 payoff matrix and depends on the combination of their selections. The P-score (“P” for punishment) is defined as the score that is given when they both select betrayal. Comparing the two groups, the mean P-score at the end of the game and the mean total score were significantly higher in the ASP group, while the rate of selection of cooperative choice in both groups did not differ significantly. The classification of the shape of the graph according to fluctuation of the P-score revealed that in the ASP group only 2 cases (6.9%) showed continuous decrease of P-score compared to 8 control cases (28.6%) demonstrating similar results. However, the reasons were thought to be different: ASP subjects presumably selected card 2 because of a preference for the number itself, whereas control subjects preferentially chose this card to enhance their chance of winning the competition. It is often difficult to diagnose ASP in the young especially when they lack the distinctive clinical features of ASD in early childhood. Given the limited number of objective tools to evaluate the cognitive characteristics of ASP subjects, the PD game might be a useful diagnostic support tool for ASP.     

Self-Fulfilling Prophecies as a Link between Men’s Facial Width-to-Height Ratio and Behavior

The facial width-to-height ratio (fWHR) has been identified as a reliable predictor of men’s behavior, with researchers focusing on evolutionary selection pressures as the underlying mechanism explaining these relationships. In this paper, we complement this approach and examine the extent to which social processes also determine the extent to which men’s fWHR serves as a behavioral cue. Specifically, we propose that observers’ treatment of target men based on the targets’ fWHR subsequently affects behavior, leading the targets to behave in ways that are consistent with the observers’ expectations (i.e., a self-fulfilling prophecy). Results from four studies demonstrate that individuals behave more selfishly when interacting with men with greater fWHRs, and this selfish behavior, in turn, elicits selfish behavior in others.     

Evidence for Mate Guarding Behavior in the Taylor’s Checkerspot Butterfly

Discerning the intricacies of mating systems in butterflies can be difficult, particularly when multiple mating strategies are employed and are cryptic and not exclusive. We observed the behavior and habitat use of 113 male Taylor’s checkerspot butterflies (Euphydryas editha taylori). We confirmed that two distinct mating strategies were exhibited; patrolling and perching. These strategies varied temporally in relation to the protandrous mating system employed. Among perching males, we recorded high site fidelity and aggressive defense of small (<5 m²) territories. This territoriality was not clearly a function of classic or non-classic resource defense (i.e., host plants or landscape), but rather appeared to constitute guarding of female pupae (virgin females). This discrete behavior is previously undocumented for this species and has rarely been observed in butterflies.     

Family Income Affects Children’s Altruistic Behavior in the Dictator Game

This study aimed to examine how family income and social distance influence young rural Chinese children’s altruistic behavior in the dictator game (DG). A total of 469 four-year-old children from eight rural areas in China, including many children left behind by parents who had migrated to urban areas for work, played the DG. Stickers comprised the resource, while recipients in the game were assumed to be either their friends or strangers, with the social distance (i.e., strangers compared to friends) as a between-subjects variable. Children donated significantly more stickers to their friends than to strangers. Moreover, children from lower income families donated more stickers than children from higher income families. However, no gender and parental migrant status differences in children’s prosocial behaviors were evident in this sample. Findings of this study suggest that children’s altruistic behaviours to peers are influenced by family characteristics since preschool age. The probable influence of local socialization practices on development and the possible adaptive significance were discussed.     

Association between coding variability in the LRP gene and the risk of late-onset Alzheimer’s disease

We have sequenced the entire (89 exons) open reading frame of the LRP gene in 12 cases of Alzheimer’s disease (AD) from Northern France. We have found no novel changes but confirm the occurrence of a polymorphism in exon 6 of the gene (A216V). This polymorphism is rare (2.8% of controls) and is in linkage equilibrium with previously reported polymorphisms. The V216 allele is negatively associated with the disease in a large case-controlled series. These data suggest that the LRP receptor may be involved in the pathobiology of AD, but the association that we report here cannot explain the previously reported genetic data implicating the LRP gene in AD. If the LRP gene is a major site of genetic variability leading to AD, there must be other biologically relevant variability in promoter or other regulatory elements of this large gene. Received: 28 December 1998 / Accepted: 1 March 1999