Coexistence of cooperation and defection in public goods games

The production of public goods by the contribution of individual volunteers is a social dilemma because an individual that does not volunteer can benefit from the public good produced by the contributions of others. Therefore it is generally believed that public goods can be produced only in the presence of repeated interactions (which allow reciprocation, reputation effects and punishment) or relatedness (kin selection). Cooperation, however, often occurs in the absence of iterations and relatedness. We show that when the production of a public good is a Volunteer's Dilemma, in which a fixed number of cooperators is necessary to produce the public good, cooperators and defectors persist in a mixed equilibrium, without iterations and without relatedness. This mixed equilibrium is absent in the N-person Prisoner's Dilemma, in which the public good is a linear function of the individual contributions. We also show that the Prisoner's Dilemma and the Volunteer's Dilemma are the two opposite extremes of a general public goods game, and that all intermediate cases can have a mixed equilibrium like the Volunteer's Dilemma. The coexistence of cooperators and defectors, therefore, is a typical outcome of most social dilemmas, which requires neither relatedness nor iterations.     

Probabilistic participation in public goods games

Voluntary participation in public goods games (PGGs) has turned out to be a simple but effective mechanism for promoting cooperation under full anonymity. Voluntary participation allows individuals to adopt a risk-aversion strategy, termed loner. A loner refuses to participate in unpromising public enterprises and instead relies on a small but fixed pay-off. This system leads to a cyclic dominance of three pure strategies, cooperators, defectors and loners, but at the same time, there remain two considerable restrictions: the addition of loners cannot stabilize the dynamics and the time average pay-off for each strategy remains equal to the pay-off of loners. Here, we introduce probabilistic participation in PGGs from the standpoint of diversification of risk, namely simple mixed strategies with loners, and prove the existence of a dynamical regime in which the restrictions ono longer hold. Considering two kinds of mixed strategies associated with participants (cooperators or defectors) and non-participants (loners), we can recover all basic evolutionary dynamics of the two strategies: dominance; coexistence; bistability; and neutrality, as special cases depending on pairs of probabilities. Of special interest is that the expected pay-off of each mixed strategy exceeds the pay-off of loners at some interior equilibrium in the coexistence region.     

Replicator dynamics of reward & reputation in public goods games

Public goods games have become the mathematical metaphor for game theoretical investigations of cooperative behavior in groups of interacting individuals. Cooperation is a conundrum because cooperators make a sacrifice to benefit others at some cost to themselves. Exploiters or defectors reap the benefits and forgo costs. Despite the fact that groups of cooperators outperform groups of defectors, Darwinian selection or utilitarian principles based on rational choice should favor defectors. In order to overcome this social dilemma, much effort has been expended for investigations pertaining to punishment and sanctioning measures against defectors. Interestingly, the complementary approach to create positive incentives and to reward cooperation has received considerably less attention—despite being heavily advocated in education and social sciences for increasing productivity or preventing conflicts. Here we show that rewards can indeed stimulate cooperation in interaction groups of arbitrary size but, in contrast to punishment, fail to stabilize it. In both cases, however, reputation is essential. The combination of reward and reputation result in complex dynamics dominated by unpredictable oscillations.     

Ecological public goods games: cooperation and bifurcation

The Public Goods Game is one of the most popular models for studying the origin and maintenance of cooperation. In its simplest form, this evolutionary game has two regimes: defection goes to fixation if the multiplication factor r is smaller than the interaction group size N, whereas cooperation goes to fixation if the multiplication factor r is larger than the interaction group size N. Hauert et al. [Hauert, C., Holmes, M., Doebeli, M., 2006a. Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc. R. Soc. Lond. B 273, 2565-2570] have introduced the Ecological Public Goods Game by viewing the payoffs from the evolutionary game as birth rates in a population dynamic model. This results in a feedback between ecological and evolutionary dynamics: if defectors are prevalent, birth rates are low and population densities decline, which leads to smaller interaction groups for the Public Goods game, and hence to dominance of cooperators, with a concomitant increase in birth rates and population densities. This feedback can lead to stable co-existence between cooperators and defectors. Here we provide a detailed analysis of the dynamics of the Ecological Public Goods Game, showing that the model exhibits various types of bifurcations, including supercritical Hopf bifurcations, which result in stable limit cycles, and hence in oscillatory co-existence of cooperators and defectors. These results show that including population dynamics in evolutionary games can have important consequences for the evolutionary dynamics of cooperation.     

Cooperation as a volunteer’s dilemma and the strategy of conflict in public goods games

Conflict and cooperation for the exploitation of public goods are usually modelled as an N‐person prisoner’s dilemma. Many social dilemmas, however, would be described more properly as a volunteer’s dilemma, in which a certain number of individuals are necessary to produce a public good. If volunteering is costly, but so is failure to produce the public good, cheaters can invade and form a stable mixed equilibrium with cooperators. The dilemma is that the benefit for the group decreases with group size because the larger the group is, the less likely it is that someone volunteers. This problem persists even in the presence of a high degree of relatedness between group members. This model provides precise, testable predictions for the stability of cooperation. It also suggests a counterintuitive but practical solution for this kind of social dilemmas: increasing the damage resulting from the failure to produce the public good increases the probability that the public good is actually produced. Adopting a strategy that entails a deliberate risk (brinkmanship), therefore, can lead to a benefit for the society without being detrimental for the individual.     

Economic game theory for mutualism and cooperation

We review recent work at the interface of economic game theory and evolutionary biology that provides new insights into the evolution of partner choice, host sanctions, partner fidelity feedback and public goods. (1) The theory of games with asymmetrical information shows that the right incentives allow hosts to screen-out parasites and screen-in mutualists, explaining successful partner choice in the absence of signalling. Applications range from ant-plants to microbiomes. (2) Contract theory distinguishes two longstanding but weakly differentiated explanations of host response to defectors: host sanctions and partner fidelity feedback. Host traits that selectively punish misbehaving symbionts are parsimoniously interpreted as pre-adaptations. Yucca-moth and legume-rhizobia mutualisms are argued to be examples of partner fidelity feedback. (3) The theory of public goods shows that cooperation in multi-player interactions can evolve in the absence of assortment, in one-shot social dilemmas among non-kin. Applications include alarm calls in vertebrates and exoenzymes in microbes.     

No effect of intraspecific relatedness on public goods cooperation in a complex community

Many organisms—notably microbes—are embedded within complex communities where cooperative behaviors in the form of excreted public goods can benefit other species. Under such circumstances, intraspecific interactions are likely to be less important in driving the evolution of cooperation. We first illustrate this idea with a simple theoretical model, showing that relatedness—the extent to which individuals with the same cooperative alleles interact with each other—has a reduced impact on the evolution of cooperation when public goods are shared between species. We test this empirically using strain of Pseudomonas aeruginosa that vary in their production of metal‐chelating siderophores in copper contaminated compost (an interspecific public good). We show that nonsiderophore producers grow poorly relative to producers under high relatedness, but this cost can be alleviated by the presence of the isogenic producer (low relatedness) and/or the compost microbial community. Hence, relatedness can become unimportant when public goods provide interspecific benefits.     

Evolution of cooperation under -person snowdrift games

In the animal world, performing a given task which is beneficial to an entire group requires the cooperation of several individuals of that group who often share the workload required to perform the task. The mathematical framework to study the dynamics of collective action is game theory. Here we study the evolutionary dynamics of cooperators and defectors in a population in which groups of individuals engage in N-person, non-excludable public goods games. We explore an N-person generalization of the well-known two-person snowdrift game. We discuss both the case of infinite and finite populations, taking explicitly into consideration the possible existence of a threshold above which collective action is materialized. Whereas in infinite populations, an N-person snowdrift game (NSG) leads to a stable coexistence between cooperators and defectors, the introduction of a threshold leads to the appearance of a new interior fixed point associated with a coordination threshold. The fingerprints of the stable and unstable interior fixed points still affect the evolutionary dynamics in finite populations, despite evolution leading the population inexorably to a monomorphic end-state. However, when the group size and population size become comparable, we find that spite sets in, rendering cooperation unfeasible.     

Invasion of cooperators in lattice populations: Linear and non-linear public good games

A generalized version of the N-person volunteer's dilemma (NVD) Game has been suggested recently for illustrating the problem of N-person social dilemmas. Using standard replicator dynamics it can be shown that coexistence of cooperators and defectors is typical in this model. However, the question of how a rare mutant cooperator could invade a population of defectors is still open.     

The evolution of payoff matrices: providing incentives to cooperate

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk-dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.     

Spatial effects in social dilemmas

Social dilemmas and the evolutionary conundrum of cooperation are traditionally studied through various kinds of game theoretical models such as the prisoner's dilemma, public goods games, snowdrift games or by-product mutualism. All of them exemplify situations which are characterized by different degrees of conflicting interests between the individuals and the community. In groups of interacting individuals, cooperators produce a common good benefitting the entire group at some cost to themselves, whereas defectors attempt to exploit the resource by avoiding the costly contributions. Based on synergistic or discounted accumulation of cooperative benefits a unifying theoretical framework was recently introduced that encompasses all games that have traditionally been studied separately (Hauert, Michor, Nowak, Doebeli, 2005. Synergy and discounting of cooperation in social dilemmas. J. Theor. Biol., in press.). Within this framework we investigate the effects of spatial structure with limited local interactions on the evolutionary fate of cooperators and defectors. The quantitative effects of space turn out to be quite sensitive to the underlying microscopic update mechanisms but, more general, we demonstrate that in prisoner's dilemma type interactions spatial structure benefits cooperation-although the parameter range is quite limited-whereas in snowdrift type interactions spatial structure may be beneficial too, but often turns out to be detrimental to cooperation.     

Simple scaling of cooperation in donor-recipient games

We present a simple argument which proves a general version of the scaling phenomenon recently observed in donor-recipient games by Tanimoto [Tanimoto, J., 2009. A simple scaling of the effectiveness of supporting mutual cooperation in donor-recipient games by various reciprocity mechanisms. BioSystems 96, 29–34].     

Cooperative investment in public goods is kin directed in communal nests of social birds

The tragedy of the commons predicts social collapse when public goods are jointly exploited by individuals attempting to maximize their fitness at the expense of other social group members. However, animal societies have evolved many times despite this vulnerability to exploitation by selfish individuals. Kin selection offers a solution to this social dilemma, but in large social groups mean relatedness is often low. Sociable weavers (Philetairus socius) live in large colonies that share the benefits of a massive communal nest, which requires individual investment for construction and maintenance. Here, we show that despite low mean kinship within colonies, relatives are spatially and socially clustered and that nest‐building males have higher local relatedness to other colony members than do non‐building males. Alternative hypotheses received little support, so we conclude that the benefits of the public good are shared with kin and that cooperative investment is, despite the large size and low relatedness of these communities, kin directed.     

Co-evolution of behaviour and social network structure promotes human cooperation

The ubiquity of cooperation in nature is puzzling because cooperators can be exploited by defectors. Recent theoretical work shows that if dynamic networks define interactions between individuals, cooperation is favoured by natural selection. To address this, we compare cooperative behaviour in multiple but independent repeated games between participants in static and dynamic networks. In the latter, participants could break their links after each social interaction. As predicted, we find higher levels of cooperation in dynamic networks. Through biased link breaking (i.e. to defectors) participants affected their social environment. We show that this link-breaking behaviour leads to substantial network clustering and we find primarily cooperators within these clusters. This assortment is remarkable because it occurred on top of behavioural assortment through direct reciprocity and beyond the perception of participants, and represents a self-organized pattern. Our results highlight the importance of the interaction between ecological context and selective pressures on cooperation.     

Ethnic divisions and public goods provision,revisited

A considerable amount of recent work in political science and economics builds from the hypothesis that ethnic heterogeneity leads to poor provision of public goods, a key component of poor governance. Much of this work cites Alesina, Baqir and Easterly as providing empirical proof. This paper argues that the findings of this article have been significantly overstated. Through a simple re-analysis of the data, it shows that ethnic diversity does not straightforwardly undermine public goods provision. Rather, at least in these data, the relationship is mixed for different public goods: ethnic diversity is related to lower provision of some public goods and to higher provision of others. In some cases, there is no clear relationship. The differences between the findings presented here and those of the original article are arguably subtle, but are worth noting because of Alesina, et al.'s important contribution to the literature.     

The effect of dispersal and neighbourhood in games of cooperation

The prisoner's dilemma (PD) and the snowdrift (SD) games are paradigmatic tools to investigate the origin of cooperation. Whereas spatial structure (e.g. nonrandom spatial distribution of strategies) present in the spatially explicit models facilitates the emergence of cooperation in the PD game, recent investigations have suggested that spatial structure can be unfavourable for cooperation in the SD game. The frequency of cooperators in a spatially explicit SD game can be lower than it would be in an infinitely large well-mixed population. However, the source of this effect cannot be identified with certainty as spatially explicit games differ from well-mixed games in two aspects: (i) they introduce spatial correlations, (ii) and limited neighbourhood. Here we extend earlier investigations to identify the source of this effect, and thus accordingly we study a spatially explicit version of the PD and SD games with varying degrees of dispersal and neighbourhood size. It was found that dispersal favours selfish individuals in both games. We calculated the frequency of cooperators at strong dispersal limit, which in concordance with the numerical results shows that it is the short range of interactions (i.e. limited neighbourhood) and not spatial correlations that decreases the frequency of cooperators in spatially explicit models of populations. Our results demonstrate that spatial correlations are always beneficial to cooperators in both the PD and SD games. We explain the opposite effect of dispersal and neighbourhood structure, and discuss the relevance of distinguishing the two effects in general.     

Stable public goods cooperation and dynamic social interactions in yeast

Despite long-standing theoretical interest in the evolution of cooperation, empirical data on the evolutionary dynamics of cooperative traits remain limited. Here, we investigate the evolutionary dynamics of a simple public goods cooperative trait, invertase secretion, using a long-term selection experiment in Saccharomyces cerevisiae. We show that average investment in cooperation remains essentially constant over a period of hundreds of generations in viscous populations with high relatedness. Average cooperation remains constant despite transient local selection for high and low levels of cooperation that generate dynamic social interactions. Natural populations of yeast show similar variation in social strategies, which is consistent with the existence of similar selective pressures on public goods cooperation in nature.     

Bounded rationality in volunteering public goods games

It is one of the fundamental problems in biology and social sciences how to maintain high levels of cooperation among selfish individuals. Theorists present an effective mechanism promoting cooperation by allowing for voluntary participation in public goods games. But Nash's theory predicts that no one can do better or worse than loners (players unwilling to join the public goods game) in the long run, and that the frequency of participants is independent of loners’ payoff. In this paper, we introduce a degree of rationality and investigate the model by means of an approximate best response dynamics. Our research shows that the payoffs of the loners have a significant effect in anonymous voluntary public goods games by this introduction and that the dynamics will drive the system to a fixed point, which is different from the Nash equilibrium. In addition, we also qualitatively explain the existing experimental results.     

Maintenance affects the stability of a two-tiered microbial 'food chain'?

Recent studies have shown that constraints on available resources may play an important role in the evolution of cooperation, especially when individuals do not posses the capacity to recognize other individuals, memory or other developed abilities, as it is the case of most unicellular organisms, algae or even plants. We analyze the evolution of cooperation in the case of a limiting resource, which is necessary for reproduction and survival. We show that, if the strategies determine a prisoner's dilemma, the outcome of the interactions may be modified by the limitation of resources allowing cooperators to invade the entire population. Analytic expressions for the region of cooperation are provided. Furthermore we derive expressions for the connection between fitness, as understood in evolutionary game theory, and resource exchanges, which may be of help to link evolutionary game theoretical results with resource based models.     

No unique effect of intergroup competition on cooperation: non-competitive thresholds are as effective as competitions between groups for increasing human cooperative behavior

Explaining cooperation remains a central topic for evolutionary theorists. Many have argued that group selection provides such an explanation: theoretical models show that intergroup competition could have given rise to cooperation that is costly for the individual. Whether group selection actually did play an important role in the evolution of human cooperation, however, is much debated. Recent experiments have shown that intergroup competitions do increase human cooperation, which has been taken as evidence for group selection as a mechanism for the evolution of cooperation. Here we challenge this standard interpretation. Competitions change the payoff structure by creating a threshold effect whereby the group that contributes more earns an additional prize, which creates some incentive for individuals to cooperate. We present four studies that disentangle competition and thresholds, and strongly suggest that it is thresholds – rather than competitions per se – that increase cooperation. Thus, prior intergroup competition experiments provide no evidence of a unique or special role for intergroup competition in promoting human cooperation, and shed no light on whether group selection shaped human evolution.