Human cooperation in social dilemmas: comparing the Snowdrift game with the Prisoner's Dilemma

Explaining the evolution of cooperation among non-relatives is one of the major challenges for evolutionary biology. In this study, we experimentally examined human cooperation in the iterated Snowdrift game (ISD), which has received little attention so far, and compared it with human cooperation in the iterated Prisoner's Dilemma (IPD), which has become the paradigm for the evolution of cooperation. We show that iteration in the ISD leads to consistently higher levels of cooperation than in the IPD. We further demonstrate that the most successful strategies known for the IPD (generous Tit-for-Tat and Pavlov) were also successfully used in the ISD. Interestingly, we found that female players cooperated significantly more often than male players in the IPD but not in the ISD. Moreover, female players in the IPD applied Tit-for-Tat-like or Pavlovian strategies significantly more often than male players, thereby achieving significantly higher pay-offs than male players did. These data demonstrate that the willingness to cooperate does not only depend on the type of the social dilemma, but also on the class of individuals involved. Altogether, our study shows that the ISD can potentially explain high levels of cooperation among non-relatives in humans. In addition, the ISD seems to reflect the social dilemma more realistically than the IPD because individuals obtain immediate direct benefits from the cooperative acts they perform and costs of cooperation are shared between cooperators.     

Evolutionary dynamics of the continuous iterated prisoner's dilemma

The iterated prisoner's dilemma (IPD) has been widely used in the biological and social sciences to model dyadic cooperation. While most of this work has focused on the discrete prisoner's dilemma, in which actors choose between cooperation and defection, there has been some analysis of the continuous IPD, in which actors can choose any level of cooperation from zero to one. Here, we analyse a model of the continuous IPD with a limited strategy set, and show that a generous strategy achieves the maximum possible payoff against its own type. While this strategy is stable in a neighborhood of the equilibrium point, the equilibrium point itself is always vulnerable to invasion by uncooperative strategies, and hence subject to eventual destabilization. The presence of noise or errors has no effect on this result. Instead, generosity is favored because of its role in increasing contributions to the most efficient level, rather than in counteracting the corrosiveness of noise. Computer simulation using a single-locus infinite alleles Gaussian mutation model suggest that outcomes ranging from a stable cooperative polymorphism to complete collapse of cooperation are possible depending on the magnitude of the mutational variance. Also, making the cost of helping a convex function of the amount of help provided makes it more difficult for cooperative strategies to invade a non-cooperative equilibrium, and for the cooperative equilibrium to resist destabilization by non-cooperative strategies. Finally, we demonstrate that a much greater degree of assortment is required to destabilize a non-cooperative equilibrium in the continuous IPD than in the discrete IPD. The continuous model outlined here suggests that incremental amounts of cooperation lead to rapid decay of cooperation and thus even a large degree of assortment will not be sufficient to allow cooperation to increase when cooperators are rare. The extreme degree of assortment required to destabilize the non-cooperative equilibrium, as well as the instability of the cooperative equilibrium, may help explain why cooperation in Prisoner's Dilemmas is so rare in nature.     

Resolving the iterated prisoner's dilemma: theory and reality

Pairs of unrelated individuals face a prisoner's dilemma if cooperation is the best mutual outcome, but each player does best to defect regardless of his partner's behaviour. Although mutual defection is the only evolutionarily stable strategy in one-shot games, cooperative solutions based on reciprocity can emerge in iterated games. Among the most prominent theoretical solutions are the so-called bookkeeping strategies, such as tit-for-tat, where individuals copy their partner's behaviour in the previous round. However, the lack of empirical data conforming to predicted strategies has prompted the suggestion that the iterated prisoner's dilemma (IPD) is neither a useful nor realistic basis for investigating cooperation. Here, we discuss several recent studies where authors have used the IPD framework to interpret their data. We evaluate the validity of their approach and highlight the diversity of proposed solutions. Strategies based on precise accounting are relatively uncommon, perhaps because the full set of assumptions of the IPD model are rarely satisfied. Instead, animals use a diverse array of strategies that apparently promote cooperation, despite the temptation to cheat. These include both positive and negative reciprocity, as well as long-term mutual investments based on 'friendships'. Although there are various gaps in these studies that remain to be filled, we argue that in most cases, individuals could theoretically benefit from cheating and that cooperation cannot therefore be explained with the concept of positive pseudo-reciprocity. We suggest that by incorporating empirical data into the theoretical framework, we may gain fundamental new insights into the evolution of mutual reciprocal investment in nature.     

Beyond the prisoner's dilemma: Toward models to discriminate among mechanisms of cooperation in nature

The iterated prisoner's dilemma game, or IPD, has now established itself as the orthodox paradigm for theoretical investigations of the evolution of cooperation; but its scope is restricted to reciprocity, which is only one of three categories of cooperation among unrelated individuals. Even within that category, a cooperative encounter has in general three phases, and the IPD has nothing to say about two of them. To distinguish among mechanisms of cooperation in nature, future theoretical work on the evolution of cooperation must distance itself from economics and develop games as a refinement of ethology's comparative approach.     

Coevolution of trustful buyers and cooperative sellers in the trust game

Many online marketplaces enjoy great success. Buyers and sellers in successful markets carry out cooperative transactions even if they do not know each other in advance and a moral hazard exists. An indispensable component that enables cooperation in such social dilemma situations is the reputation system. Under the reputation system, a buyer can avoid transacting with a seller with a bad reputation. A transaction in online marketplaces is better modeled by the trust game than other social dilemma games, including the donation game and the prisoner's dilemma. In addition, most individuals participate mostly as buyers or sellers; each individual does not play the two roles with equal probability. Although the reputation mechanism is known to be able to remove the moral hazard in games with asymmetric roles, competition between different strategies and population dynamics of such a game are not sufficiently understood. On the other hand, existing models of reputation-based cooperation, also known as indirect reciprocity, are based on the symmetric donation game. We analyze the trust game with two fixed roles, where trustees (i.e., sellers) but not investors (i.e., buyers) possess reputation scores. We study the equilibria and the replicator dynamics of the game. We show that the reputation mechanism enables cooperation between unacquainted buyers and sellers under fairly generous conditions, even when such a cooperative equilibrium coexists with an asocial equilibrium in which buyers do not buy and sellers cheat. In addition, we show that not many buyers may care about the seller's reputation under cooperative equilibrium. Buyers' trusting behavior and sellers' reputation-driven cooperative behavior coevolve to alleviate the social dilemma.     

Asymmetric interaction will facilitate the evolution of cooperation

Explaining the evolution of cooperation remains one of the greatest problems for both biology and social science. The classical theories of cooperation suggest that cooperation equilibrium or evolutionary stable strategy between partners can be maintained through genetic similarity or reciprocity relatedness. These classical theories are based on an assumption that partners interact symmetrically with equal payoffs in a game of cooperation interaction. However, the payoff between partners is usually not equal and therefore they often interact asymmetrically in real cooperative systems. With the Hawk-Dove model, we find that the probability of cooperation between cooperative partners will depend closely on the payoff ratio. The higher the payoff ratio between recipients and cooperative actors, the greater will be the probability of cooperation interaction between involved partners. The greatest probability of conflict between cooperative partners will occur when the payoff between partners is equal. The results show that this asymmetric relationship is one of the key dynamics of the evolution of cooperation, and that pure cooperation strategy (i.e., Nash equilibrium) does not exist in asymmetrical cooperation systems, which well explains the direct conflict observed in almost all of the well documented cooperation systems. The model developed here shows that the cost-to-benefit ratio of cooperation is also negatively correlated with the probability of cooperation interaction. A smaller cost-to-benefit ratio of cooperation might be created by the limited dispersal ability or exit cost of the partners involved, and it will make the punishment of the non-cooperative individuals by the recipient more credible, and therefore make it more possible to maintain stable cooperation interaction.     

The continuous prisoner's dilemma and the evolution of cooperation through reciprocal altruism with variable investment

Understanding the evolutionary origin and persistence of cooperative behavior is a fundamental biological problem. The standard "prisoner's dilemma," which is the most widely adopted framework for studying the evolution of cooperation through reciprocal altruism between unrelated individuals, does not allow for varying degrees of cooperation. Here we study the continuous iterated prisoner's dilemma, in which cooperative investments can vary continuously in each round. This game has been previously considered for a class of reactive strategies in which current investments are based on the partner's previous investment. In the standard iterated prisoner's dilemma, such strategies are inferior to strategies that take into account both players' previous moves, as is exemplified by the evolutionary dominance of "Pavlov" over "tit for tat." Consequently, we extend the analysis of the continuous prisoner's dilemma to a class of strategies in which current investments depend on previous payoffs and, hence, on both players' previous investments. We show, both analytically and by simulation, that payoff-based strategies, which embody the intuitively appealing idea that individuals invest more in cooperative interactions when they profit from these interactions, provide a natural explanation for the gradual evolution of cooperation from an initially noncooperative state and for the maintenance of cooperation thereafter.     

When in Rome,do as the Romans do: the coevolution of altruistic punishment,conformist learning,and cooperation

We model the coevolution of behavioral strategies and social learning rules in the context of a cooperative dilemma, a situation in which individuals must decide whether or not to subordinate their own interests to those of the group. There are two learning rules in our model, conformism and payoff-dependent imitation, which evolve by natural selection, and three behavioral strategies, cooperate, defect, and cooperate, plus punish defectors, which evolve under the influence of the prevailing learning rules. Group and individual level selective pressures drive evolution.We also simulate our model for conditions that approximate those in which early hominids lived. We find that conformism can evolve when the only problem that individuals face is a cooperative dilemma, in which prosocial behavior is always costly to the individual. Furthermore, the presence of conformists dramatically increases the group size for which cooperation can be sustained. The results of our model are robust: they hold even when migration rates are high, and when conflict among groups is infrequent.     

Selection for cheating across disparate environments in the legume‐rhizobium mutualism

The primary dilemma in evolutionarily stable mutualisms is that natural selection for cheating could overwhelm selection for cooperation. Cheating need not entail parasitism; selection favours cheating as a quantitative trait whenever less‐cooperative partners are more fit than more‐cooperative partners. Mutualisms might be stabilised by mechanisms that direct benefits to more‐cooperative individuals, which counter selection for cheating; however, empirical evidence that natural selection favours cheating in mutualisms is sparse. We measured selection on cheating in single‐partner pairings of wild legume and rhizobium lineages, which prevented legume choice. Across contrasting environments, selection consistently favoured cheating by rhizobia, but did not favour legumes that provided less benefit to rhizobium partners. This is the first simultaneous measurement of selection on cheating across both host and symbiont lineages from a natural population. We empirically confirm selection for cheating as a source of antagonistic coevolutionary pressure in mutualism and a biological dilemma for models of cooperation.     

The continuous Prisoner's dilemma: II. Linear reactive strategies with noise.

We present a general model for the Continuous Prisoner's Dilemma and study the effect of errors. We find that cooperative strategies that can resist invasion by defectors are optimistic (make high initial offers), generous (always offer more cooperation than the partner did in the previous round) and uncompromising (offer full cooperation only if the partner does). A necessary condition for the emergence of cooperation in the continuous Prisoner's Dilemma with noise is b (1-p)>c, where b and c denote, respectively, the benefit and cost of cooperation, while p is the error rate. This relation can be reformulated as an error threshold: cooperation can only emerge if the probability of making a mistake is below a critical value. We note, however, that cooperation in the continuous Prisoner's Dilemma with noise does not seem to be evolutionarily stable: while it is possible to find cooperative strategies that resist invasion by defectors, such cooperators are generally invaded by more cooperative strategies which eventually yield to defectors. Thus, the long-term evolution of the continuous Prisoner's Dilemma is either characterized by unending cycles or by stable polymorphisms of cooperators and defectors.     

The Effects of Extra-Somatic Weapons on the Evolution of Human Cooperation towards Non-Kin

Human cooperation and altruism towards non-kin is a major evolutionary puzzle, as is ‘strong reciprocity’ where no present or future rewards accrue to the co-operator/altruist. Here, we test the hypothesis that the development of extra-somatic weapons could have influenced the evolution of human cooperative behaviour, thus providing a new explanation for these two puzzles. Widespread weapons use could have made disputes within hominin groups far more lethal and also equalized power between individuals. In such a cultural niche non-cooperators might well have become involved in such lethal disputes at a higher frequency than cooperators, thereby increasing the relative fitness of genes associated with cooperative behaviour. We employ two versions of the evolutionary Iterated Prisoner''s Dilemma (IPD) model – one where weapons use is simulated and one where it is not. We then measured the performance of 25 IPD strategies to evaluate the effects of weapons use on them. We found that cooperative strategies performed significantly better, and non-cooperative strategies significantly worse, under simulated weapons use. Importantly, the performance of an ‘Always Cooperate’ IPD strategy, equivalent to that of ‘strong reciprocity’, improved significantly more than that of all other cooperative strategies. We conclude that the development of extra-somatic weapons throws new light on the evolution of human altruistic and cooperative behaviour, and particularly ‘strong reciprocity’. The notion that distinctively human altruism and cooperation could have been an adaptive trait in a past environment that is no longer evident in the modern world provides a novel addition to theory that seeks to account for this major evolutionary puzzle.     

从合作的进化探讨植物与传粉者的相互作用

合作的进化为研究植物–传粉者相互关系提供了新的视角。植物与传粉者通过"报酬换服务"建立种间合作关系。这一合作关系从建立、维持到解体面临着3个关键问题:(1)在植物和传粉者不了解对方质量信息时,双方如何选择出最适伙伴,进而建立合作关系;(2)合作方如何限制欺骗策略(比如,盗蜜和欺骗性传粉)的扩散以维持合作关系;(3)什么过程可导致传粉合作关系的解体。植物与传粉者间信号博弈或筛选博弈可促进二者合作关系的建立。面对欺骗策略,传粉者和植物分别采用伙伴选择机制和防御机制加以应对。合作者与欺骗者的稳定共存也有助于植物–传粉者合作的维持。从合作转向对抗、转向新的伙伴和合作放弃3个过程可导致植物–传粉者的合作关系的解体。植物与传粉者合作关系的理论预期已经得到了部分实验结果支持,深化了我们对植物与传粉者合作过程中关键机制的理解。在今后的研究中,需要进一步探讨以下问题:(1)传粉者对植物信号诚实性的选择作用和植物对传粉者的筛选作用;(2)植物与传粉者各自应对欺骗策略的可能机制及其相对重要性;(3)合作者与欺骗者稳定共存的机制;(4)植物与传粉者合作系统对全球变化的响应。     

Spiking neural networks with different reinforcement learning (RL) schemes in a multiagent setting

This paper investigates the effectiveness of spiking agents when trained with reinforcement learning (RL) in a challenging multiagent task. In particular, it explores learning through reward-modulated spike-timing dependent plasticity (STDP) and compares it to reinforcement of stochastic synaptic transmission in the general-sum game of the Iterated Prisoner's Dilemma (IPD). More specifically, a computational model is developed where we implement two spiking neural networks as two "selfish" agents learning simultaneously but independently, competing in the IPD game. The purpose of our system (or collective) is to maximise its accumulated reward in the presence of reward-driven competing agents within the collective. This can only be achieved when the agents engage in a behaviour of mutual cooperation during the IPD. Previously, we successfully applied reinforcement of stochastic synaptic transmission to the IPD game. The current study utilises reward-modulated STDP with eligibility trace and results show that the system managed to exhibit the desired behaviour by establishing mutual cooperation between the agents. It is noted that the cooperative outcome was attained after a relatively short learning period which enhanced the accumulation of reward by the system. As in our previous implementation, the successful application of the learning algorithm to the IPD becomes possible only after we extended it with additional global reinforcement signals in order to enhance competition at the neuronal level. Moreover it is also shown that learning is enhanced (as indicated by an increased IPD cooperative outcome) through: (i) strong memory for each agent (regulated by a high eligibility trace time constant) and (ii) firing irregularity produced by equipping the agents' LIF neurons with a partial somatic reset mechanism.     

Physical attractiveness and cooperation in a prisoner's dilemma game

The modulating role of age on the relationship between physical attractiveness and cooperativeness in a prisoner's dilemma game (PDG) was investigated. Previous studies have shown that physical attractiveness is negatively related to cooperative choices among young men but not young women. Following the argument that the negative relationship between physical attractiveness and cooperation is a product of short-term mating strategies among attractive men, we predicted that this relationship is unique to young men and absent among women and older men. We tested this hypothesis with 175 participants (aged 22–69 years). The results showed that physical attractiveness was negatively related to cooperative behavior among young men but not among women or older men. We further observed that the negative relationship between physical attractiveness and cooperation among young men was particularly strong when attractiveness was judged by women.     

Are there really no evolutionarily stable strategies in the iterated prisoner's dilemma?

The evolutionary form of the iterated prisoner's dilemma (IPD) is a repeated game where players strategically choose whether to cooperate with or exploit opponents and reproduce in proportion to game success. It has been widely used to study the evolution of cooperation among selfish agents. In the past 15 years, researchers proved over a series of papers that there is no evolutionarily stable strategy (ESS) in the IPD when players maintain long-term relationships. This makes it difficult to make predictions about what strategies can actually persist as prevalent in a population over time. Here, we show that this no ESS finding may be a mathematical technicality, relying on implausible players who are "too perfect" in that their probability of cooperating on any move is arbitrarily close to either 0 or 1. Specifically, in the no ESS proof, all strategies were allowed, meaning that after a strategy X experiences any history H, X cooperates with an unrestricted probability p (X, H) where 0< or =p (X, H)< or =1. Here, we restrict strategies to the set S in which X is a member of S [corrected] if after any H, X cooperates with a restricted probability p (X, H) where e< or =p (X, H)< or =1-e and 0相似文献   

Schoolchildren cooperate more successfully with non-kin than with siblings

Cooperation plays a key role in the development of advanced societies and can be stabilized through shared genes (kinship) or reciprocation. In humans, cooperation among kin occurs more readily than cooperation among non-kin. In many organisms, cooperation can shift with age (e.g. helpers at the nest); however, little is known about developmental shifts between kin and non-kin cooperation in humans. Using a cooperative game, we show that 3- to 10-year-old French schoolchildren cooperated less successfully with siblings than with non-kin children, whether or not non-kin partners were friends. Furthermore, children with larger social networks cooperated better and the perception of friendship among non-friends improved after cooperating. These results contrast with the well-established preference for kin cooperation among adults and indicate that non-kin cooperation in humans might serve to forge and extend non-kin social relationships during middle childhood and create opportunities for future collaboration beyond kin. Our results suggest that the current view of cooperation in humans may only apply to adults and that future studies should focus on how and why cooperation with different classes of partners might change during development in humans across cultures as well as other long-lived organisms.     

Cooperation among Norway Rats: The Importance of Visual Cues for Reciprocal Cooperation,and the Role of Coercion

Some animals reciprocate help, but the underlying proximate mechanisms are largely unclear. Norway rats (Rattus norvegicus) have been shown to cooperate in a variant of the iterated prisoner's dilemma paradigm, yet it is unknown which sensory modalities they use. Visual information is often implicitly assumed to play a major role in social interactions, but primarily nocturnal species such as Norway rats may rely on different cues when deciding to reciprocate received help. We used an instrumental cooperative task to compare the test rats' propensity to reciprocate received help between two experimental conditions, with and without visual information exchange between social partners. Our results show that visual information is not required for reciprocal cooperation among social partners because even when it was lacking, test rats provided food significantly earlier to partners that had helped them to obtain food before than to those that had not done so. The mean decision speed did not differ between the two experimental conditions, with or without visual information. Social partners sometimes showed aggressive behaviour towards focal test individuals. When including this in the analyses to assess the possible role of aggression as a trigger of cooperation, aggression received from cooperators apparently reduced the cooperation propensity, whereas aggression received from defectors increased it. Hence, in addition to reciprocity, coercion seems to provide additional means to generate altruistic help in Norway rats.     

Simple adaptive strategy wins the prisoner's dilemma

The prisoner's dilemma has become the leading paradigm to explain the evolution of cooperation among selfish individuals. Here, we present an adaptive strategy that implements new mechanisms to process information about past encounters. The history of moves is summarized in an internal state which then determines the subsequent move. This enables the strategy to adjust its decisions to the character of the current opponent and to adapt the most promising strategic behavior. For this reason, we call such strategies Adaptor. Through evolutionary simulations, we demonstrate that the concept of Adaptor leads to strategic patterns that are (a) highly cooperative when playing against kin, (b) stable in a sense that goes far beyond the concept of evolutionary stability, (c) robust to environmental changes, i.e. variations of the parameter values and finally (d) superior in performance to the most prominent strategies in the literature.     

The evolution of punishment and apology: an iterated prisoner's dilemma model

Recently, behaviors that seem to function as punishment or apology have been reported among non-human primates as well as humans. Such behaviors appear to play an important role in maintaining cooperation between individuals. Therefore, the evolution of these behaviors should be examined from the viewpoint of the evolution of cooperation. The iterated prisoner's dilemma (IPD) game is generally considered to be a standard model for the evolution of cooperation. In the present study, strategies accompanied by punishment-like attacks or apology-like behavior were introduced into the common IPD simulation. Punishment and apology were represented by the P signal and the AS signal given immediately after defection. A strategy with the P and AS signals, named the pPAS strategy, was proved to be an evolutionarily stable strategy under certain conditions. Numerical simulations were carried out according to different assigned values of the costs of punishment and apology. The simulations showed that pPAS could dominate the population (1) when the cost of giving P is relatively small, (2) when the cost of receiving P is relatively large, or (3) when the cost of giving AS is relatively large. The relative cost of giving AS had the clearest effect on the success of pPAS. pPAS can dominate the population even when a dominance asymmetry of the costs between two players was introduced. The present results suggest the possible evolution of social behaviors like punishment or apology as a means of maintaining cooperation. This revised version was published online in November 2006 with corrections to the Cover Date.     

HORIZONTAL GENE TRANSFER AND THE EVOLUTION OF BACTERIAL COOPERATION

Bacteria frequently exhibit cooperative behaviors but cooperative strains are vulnerable to invasion by cheater strains that reap the benefits of cooperation but do not perform the cooperative behavior themselves. Bacterial genomes often contain mobile genetic elements such as plasmids. When a gene for cooperative behavior exists on a plasmid, cheaters can be forced to cooperate by infection with this plasmid, rescuing cooperation in a population in which mutation or migration has allowed cheaters to arise. Here we introduce a second plasmid that does not code for cooperation and show that the social dilemma repeats itself at the plasmid level in both within‐patch and metapopulation scenarios, and under various scenarios of plasmid incompatibility. Our results suggest that although plasmid carriage of cooperative genes can provide a transient defense against defection in structured environments, plasmid and chromosomal defection remain the only stable strategies in an unstructured environment. We discuss our results in the light of recent bioinformatic evidence that cooperative genes are overrepresented on mobile elements.