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.     

Public goods games with reward in finite populations

Public goods games paraphrase the problem of cooperation in game theoretical terms. Cooperators contribute to a public good and thereby increase the welfare of others at a cost to themselves. Defectors consume the public good but do not pay its cost and therefore outperform cooperators. Hence, according to genetic or cultural evolution, defectors should be favored and the public good disappear – despite the fact that groups of cooperators are better off than groups of defectors. The maximization of short term individual profits causes the demise of the common resource to the detriment of all. This outcome can be averted by introducing incentives to cooperate. Negative incentives based on the punishment of defectors efficiently stabilize cooperation once established but cannot initiate cooperation. Here we consider the complementary case of positive incentives created by allowing individuals to reward those that contribute to the public good. The finite-population stochastic dynamics of the public goods game with reward demonstrate that reward initiates cooperation by providing an escape hatch out of states of mutual defection. However, in contrast to punishment, reward is unable to stabilize cooperation but, instead, gives rise to a persistent minority of cooperators.     

The Increased Risk of Joint Venture Promotes Social Cooperation

The joint venture of many members is common both in animal world and human society. In these public enterprizes, highly cooperative groups are more likely to while low cooperative groups are still possible but not probable to succeed. Existent literature mostly focuses on the traditional public goods game, in which cooperators create public wealth unconditionally and benefit all group members unbiasedly. We here institute a model addressing this public goods dilemma with incorporating the public resource foraging failure risk. Risk-averse individuals tend to lead a autarkic life, while risk-preferential ones tend to participate in the risky public goods game. For participants, group''s success relies on its cooperativeness, with increasing contribution leading to increasing success likelihood. We introduce a function with one tunable parameter to describe the risk removal pattern and study in detail three representative classes. Analytical results show that the widely replicated population dynamics of cyclical dominance of loner, cooperator and defector disappear, while most of the time loners act as savors while eventually they also disappear. Depending on the way that group''s success relies on its cooperativeness, either cooperators pervade the entire population or they coexist with defectors. Even in the later case, cooperators still hold salient superiority in number as some defectors also survive by parasitizing. The harder the joint venture succeeds, the higher level of cooperation once cooperators can win the evolutionary race. Our work may enrich the literature concerning the risky public goods games.     

Evolutionary games and population dynamics: maintenance of cooperation in public goods games

The emergence and abundance of cooperation in nature poses a tenacious and challenging puzzle to evolutionary biology. Cooperative behaviour seems to contradict Darwinian evolution because altruistic individuals increase the fitness of other members of the population at a cost to themselves. Thus, in the absence of supporting mechanisms, cooperation should decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the Prisoner's Dilemma and public goods games. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Here, we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation. In public goods games, cooperation can gain a foothold if the population density depends on the average population payoff. Decreasing population densities, due to defection leading to small payoffs, results in smaller interaction group sizes in which cooperation can be favoured. This feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games. However, this mechanism fails for pairwise Prisoner's Dilemma interactions and the population is driven to extinction. Our model represents natural extension of replicator dynamics to populations of varying densities.     

Group-size diversity in public goods games

Public goods games are models of social dilemmas where cooperators pay a cost for the production of a public good while defectors free ride on the contributions of cooperators. In the traditional framework of evolutionary game theory, the payoffs of cooperators and defectors result from interactions in groups formed by binomial sampling from an infinite population. Despite empirical evidence showing that group-size distributions in nature are highly heterogeneous, most models of social evolution assume that the group size is constant. In this article, I remove this assumption and explore the effects of having random group sizes on the evolutionary dynamics of public goods games. By a straightforward application of Jensen's inequality, I show that the outcome of general nonlinear public goods games depends not only on the average group size but also on the variance of the group-size distribution. This general result is illustrated with two nonlinear public goods games (the public goods game with discounting or synergy and the N-person volunteer's dilemma) and three different group-size distributions (Poisson, geometric, and Waring). The results suggest that failing to acknowledge the natural variation of group sizes can lead to an underestimation of the actual level of cooperation exhibited in evolving populations.     

Pattern formation and chaos in spatial ecological public goodsgames

Cooperators and defectors can coexist in ecological public goods games. When the game is played in two-dimensional continuous space, a reaction diffusion model produces highly irregular dynamics, in which cooperators and defectors survive in ever-changing configurations (Wakano et al., 2009. Spatial dynamics of ecological public goods. Proc. Natl. Acad. Sci. 106, 7910-7914). The dynamics is related to the formation of Turing patterns, but the origin of the irregular dynamics is not well understood. In this paper, we present a classification of the spatio-temporal dynamics based on the dispersion relation, which reveals that the spontaneous pattern formation can be attributed to the dynamical interplay between two linearly unstable modes: temporal instability arising from a Hopf-bifurcation and spatial instability arising from a Turing-bifurcation. Moreover, we provide a detailed analysis of the highly irregular dynamics through Fourier analysis, the break-down of symmetry, the maximum Lyapunov exponent, and the excitability of the reaction-term dynamics. All results clearly support that the observed irregular dynamics qualifies as spatio-temporal chaos. A particularly interesting type of chaotic dynamics, which we call intermittent bursts, clearly demonstrates the effects of the two unstable modes where (local) periods of stasis alternate with rapid changes that may induce local extinction.     

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.     

Reputation-based partner choice is an effective alternative to indirect reciprocity in solving social dilemmas

When group interests clash with individual ones, maintaining cooperation poses a problem. However, cooperation can be facilitated by introducing reputational incentives. Through indirect reciprocity, people who cooperate in a social dilemma are more likely to receive cooperative acts from others. Another mechanism that enhances group cooperation is reputation-based partner choice, or competitive altruism. According to this framework, cooperators benefit via increased access to cooperative partners. Our study compared the effectiveness of indirect reciprocity and competitive altruism in re-establishing cooperation after the typical decline found during repeated public goods games. Twenty groups of four participants first played a series of public goods games, which confirmed the expected decline. Subsequently, public goods games were alternated with either indirect reciprocity games (in which participants had an opportunity to give to another individual from whom they would never receive a direct return) or competitive altruism games (in which they could choose partners for directly reciprocal interactions). We found that public goods game contributions increased when interspersed with competitive altruism games; they were also higher than in public goods games interspersed with indirect reciprocity games. Investing in reputation by increasing contributions to public goods was a profitable strategy in that it increased returns in subsequent competitive altruism and indirect reciprocity games. There was also some evidence that these returns were greater under competitive altruism than indirect reciprocity. Our findings indicate that strategic reputation building through competitive altruism provides an effective alternative to indirect reciprocity as a means for restoring cooperation in social dilemmas.     

When Punishment Pays

Explaining cooperation in groups remains a key problem because reciprocity breaks down between more than two. Punishing individuals who contribute little provides a potential answer but changes the dilemma to why pay the costs of punishing which, like cooperation itself, provides a public good. Nevertheless, people are observed to punish others in behavioural economic games, posing a problem for existing theory which highlights the difficulty in explaining the spread and persistence of punishment. Here, I consider the apparent mismatch between theory and evidence and show by means of instructive analysis and simulation how much of the experimental evidence for punishment comes from scenarios in which punishers may expect to obtain a net benefit from punishing free-riders. In repeated games within groups, punishment works by imposing costs on defectors so that it pays them to switch to cooperating. Both punishers and non-punishers then benefit from the resulting increase in cooperation, hence investing in punishment can constitute a social dilemma. However, I show the conditions in which the benefits of increased cooperation are so great that they more than offset the costs of punishing, thereby removing the temptation to free-ride on others'' investments and making punishment explicable in terms of direct self-interest. Crucially, this is because of the leveraging effect imposed in typical studies whereby people can pay a small cost to inflict a heavy loss on a punished individual. In contrast to previous models suggesting punishment is disadvantaged when rare, I show it can invade until it comes into a producer-scrounger equilibrium with non-punishers. I conclude that adding punishment to an iterated public goods game can solve the problem of achieving cooperation by removing the social dilemma.     

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.     

Exploring the effects of working for endowments on behaviour in standard economic games

In recent years, significant advances have been made in understanding the adaptive (ultimate) and mechanistic (proximate) explanations for the evolution and maintenance of cooperation. Studies of cooperative behaviour in humans invariably use economic games. These games have provided important insights into the mechanisms that maintain economic and social cooperation in our species. However, they usually rely on the division of monetary tokens which are given to participants by the investigator. The extent to which behaviour in such games may reflect behaviour in the real world of biological markets--where money must be earned and behavioural strategies incur real costs and benefits--is unclear. To provide new data on the potential scale of this problem, we investigated whether people behaved differently in two standard economic games (public goods game and dictator game) when they had to earn their monetary endowments through the completion of dull or physically demanding tasks, as compared with simply being given the endowment. The requirement for endowments to be 'earned' through labour did not affect behaviour in the dictator game. However, the requirement to complete a dull task reduced cooperation in the public goods game among the subset of participants who were not familiar with game theory. There has been some effort to test whether the conclusions drawn from standard, token-based cooperation games adequately reflect cooperative behaviour 'in the wild.' However, given the almost total reliance on such games to study cooperation, more exploration of this issue would be welcome. Our data are not unduly worrying, but they do suggest that further exploration is needed if we are to make general inferences about human behaviour from the results of structured economic games.     

Social immunity of the family: parental contributions to a public good modulated by brood size

Social immunity refers to any immune defence that benefits others, besides the individual that mounts the response. Since contributions to social immunity are known to be personally costly, they are contributions to a public good. However, individuals vary in their contributions to this public good and it is unclear why. Here we investigate whether they are responding to contributions made by others with experiments on burying beetle (Nicrophorus vespilloides) families. In this species, females, males and larvae each contribute to social immunity through the application of antimicrobial exudates upon the carrion breeding resource. We show experimentally that mothers reduce their contributions to social immunity when raising large broods, and test two contrasting hypotheses to explain why. Either mothers are treating social immunity as a public good, investing less in social immunity when their offspring collectively contribute more, or mothers are trading off investment in social immunity with investment in parental care. Overall, our experiments yield no evidence to support the existence of a trade-off between social immunity and other parental care traits: we found no evidence of a trade-off in terms of time allocated to each activity, nor did the relationship between social immunity and brood size change with female condition. Instead, and consistent with predictions from models of public goods games, we found that higher quality mothers contributed more to social immunity. Therefore our results suggest that mothers are playing a public goods game with their offspring to determine their personal contribution to the defence of the carrion breeding resource.     

The social evolution of dispersal with public goods cooperation

Selection can favour the evolution of individually costly dispersal if this alleviates competition between relatives. However, conditions that favour altruistic dispersal also mediate selection for other social behaviours, such as public goods cooperation, which in turn is likely to mediate dispersal evolution. Here, we investigate – both experimentally (using bacteria) and theoretically – how social habitat heterogeneity (i.e. the distribution of public goods cooperators and cheats) affects the evolution of dispersal. In addition to recovering the well‐known theoretical result that the optimal level of dispersal increases with genetic relatedness of patch mates, we find both mathematically and experimentally that dispersal is always favoured when average patch occupancy is low, but when average patch occupancy is high, the presence of public goods cheats greatly alters selection for dispersal. Specifically, when public goods cheats are localized to the home patch, higher dispersal rates are favoured, but when cheats are present throughout available patches, lower dispersal rates are favoured. These results highlight the importance of other social traits in driving dispersal evolution.     

Evolutionary dynamics of interlinked public goods traits: an experimental study of siderophore production in Pseudomonas aeruginosa

Public goods cooperation is common in microbes, and there is much interest in understanding how such traits evolve. Research in recent years has identified several important factors that shape the evolutionary dynamics of such systems, yet few studies have investigated scenarios involving interactions between multiple public goods. Here, we offer general predictions about the evolutionary trajectories of two public goods traits having positive, negative or neutral regulatory influence on one another's expression, and we report on a test of some of our predictions in the context of Pseudomonas aeruginosa's production of two interlinked iron‐scavenging siderophores. First, we confirmed that both pyoverdine and pyochelin siderophores do operate as public goods under appropriate environmental conditions. We then tracked their production in lines experimentally evolved under different iron‐limitation regimes known to favour different siderophore expression profiles. Under strong iron limitation, where pyoverdine represses pyochelin, we saw a decline in pyoverdine and a concomitant increase in pyochelin – consistent with expansion of pyoverdine‐defective cheats derepressed for pyochelin. Under moderate iron limitation, pyochelin declined – again consistent with an expected cheat invasion scenario – but there was no concomitant shift in pyoverdine because cross‐suppression between the traits is unidirectional only. Alternating exposure to strong and moderate iron limitation caused qualitatively similar though lesser shifts compared to the constant‐environment regimes. Our results confirm that the regulatory interconnections between public goods traits can significantly modulate the course of evolution, yet also suggest how we can start to predict the impacts such complexities will have on phenotypic divergence and community stability.     

Evolutionary dynamics of strategic behavior in a collective-risk dilemma

A collective-risk social dilemma arises when a group must cooperate to reach a common target in order to avoid the risk of collective loss while each individual is tempted to free-ride on the contributions of others. In contrast to the prisoners' dilemma or public goods games, the collective-risk dilemma encompasses the risk that all individuals lose everything. These characteristics have potential relevance for dangerous climate change and other risky social dilemmas. Cooperation is costly to the individual and it only benefits all individuals if the common target is reached. An individual thus invests without guarantee that the investment is worthwhile for anyone. If there are several subsequent stages of investment, it is not clear when individuals should contribute. For example, they could invest early, thereby signaling their willingness to cooperate in the future, constantly invest their fair share, or wait and compensate missing contributions. To investigate the strategic behavior in such situations, we have simulated the evolutionary dynamics of such collective-risk dilemmas in a finite population. Contributions depend individually on the stage of the game and on the sum of contributions made so far. Every individual takes part in many games and successful behaviors spread in the population. It turns out that constant contributors, such as constant fair sharers, quickly lose out against those who initially do not contribute, but compensate this in later stages of the game. In particular for high risks, such late contributors are favored.     

Shame and honour drive cooperation

Can the threat of being shamed or the prospect of being honoured lead to greater cooperation? We test this hypothesis with anonymous six-player public goods experiments, an experimental paradigm used to investigate problems related to overusing common resources. We instructed the players that the two individuals who were least generous after 10 rounds would be exposed to the group. As the natural antithesis, we also test the effects of honour by revealing the identities of the two players who were most generous. The non-monetary, reputational effects induced by shame and honour each led to approximately 50 per cent higher donations to the public good when compared with the control, demonstrating that both shame and honour can drive cooperation and can help alleviate the tragedy of the commons.     

Unpredictability induced by unfocused games in evolutionary game dynamics

Evolutionary game theory is a basis of replicator systems and has applications ranging from animal behavior and human language to ecosystems and other hierarchical network systems. Most studies in evolutionary game dynamics have focused on a single game, but, in many situations, we see that many games are played simultaneously. We construct a replicator equation with plural games by assuming that a reward of a player is a simple summation of the reward of each game. Even if the numbers of the strategies of the games are different, its dynamics can be described in one replicator equation. We here show that when players play several games at the same time, the fate of a single game cannot be determined without knowing the structures of the whole other games. The most absorbing fact is that even if a single game has a ESS (evolutionary stable strategy), the relative frequencies of strategies in the game does not always converge to the ESS point when other games are played simultaneously.     

A cooperative virulence plasmid imposes a high fitness cost under conditions that induce pathogenesis

Harbouring a plasmid often imposes a fitness cost on the bacterial host. Motivated by implications for public health, the majority of studies on plasmid cost are focused on elements that impart antibiotic resistance. Plasmids, however, can provide a wide range of ecologically important phenotypes to their bacterial hosts-such as virulence, specialized catabolism and metal resistance. The Agrobacterium tumefaciens tumour-inducing (Ti) plasmid confers both the ability to infect dicotyledonous plants and to catabolize the metabolites that plants produce as a result of being infected. We demonstrate that this virulence and catabolic plasmid imposes a measurable fitness cost on host cells under resource-limiting, but not resource replete, environmental conditions. Additionally, we show that the expression of Ti-plasmid-borne pathogenesis genes necessary to initiate cooperative pathogenesis is extremely costly to the host cell. The benefits of agrobacterial pathogenesis stem from the catabolism of public goods produced by infected host plants. Thus, the virulence-plasmid-dependent costs we demonstrate constitute costs of cooperation typically associated with the ability to garner the benefits of cooperation. Interestingly, genotypes that harbour derived opine catabolic plasmids minimize this trade-off, and are thus able to freeload upon the pathogenesis initiated by other individuals.     

Evolutionary Stability in the Asymmetric Volunteer's Dilemma

It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer''s dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a “strong” player is greater than the “weak” players in the model of Diekmann (1993). This contradicts Selten''s (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.     

Cooperation in Microbial Populations: Theory and Experimental Model Systems

Cooperative behavior, the costly provision of benefits to others, is common across all domains of life. This review article discusses cooperative behavior in the microbial world, mediated by the exchange of extracellular products called public goods. We focus on model species for which the production of a public good and the related growth disadvantage for the producing cells are well described. To unveil the biological and ecological factors promoting the emergence and stability of cooperative traits we take an interdisciplinary perspective and review insights gained from both mathematical models and well-controlled experimental model systems. Ecologically, we include crucial aspects of the microbial life cycle into our analysis and particularly consider population structures where ensembles of local communities (subpopulations) continuously emerge, grow, and disappear again. Biologically, we explicitly consider the synthesis and regulation of public good production. The discussion of the theoretical approaches includes general evolutionary concepts, population dynamics, and evolutionary game theory. As a specific but generic biological example, we consider populations of Pseudomonas putida and its regulation and use of pyoverdines, iron scavenging molecules, as public goods. The review closes with an overview on cooperation in spatially extended systems and also provides a critical assessment of the insights gained from the experimental and theoretical studies discussed. Current challenges and important new research opportunities are discussed, including the biochemical regulation of public goods, more realistic ecological scenarios resembling native environments, cell-to-cell signaling, and multispecies communities.