Cooperation In Public Goods Game Research Articles

Constructive agents nullify the ability of destructive agents to foster cooperation in public goods games.

Existing studies have revealed a paradoxical phenomenon in public goods games, wherein destructive agents, harming both cooperators and defectors, can unexpectedly bolster cooperation. Building upon this intriguing premise, our paper introduces a novel concept: constructive agents, which confer additional benefits to both cooperators and defectors. We investigate the impact of these agents on cooperation dynamics within the framework of public goods games. Employing replicator dynamics, we find that unlike destructive agents, the mere presence of constructive agents does not significantly alter the defective equilibrium. However, when the benefits from constructive agents are outweighed by the damage inflicted by destructive agents, the addition of constructive agents does not affect the ability of destructive agents to sustain cooperation. In this scenario, cooperators can be maintained through a cyclic dominance between cooperators, defectors, and destructive agents, with constructive agents adding complexity but not fundamentally changing the equilibrium. Conversely, if the benefits from constructive agents surpass the harm caused by destructive agents, the presence of constructive agents nullifies the ability of destructive agents to foster cooperation. Our results highlight the nuanced role of constructive agents in cooperation dynamics, emphasizing the necessity of carefully assessing incentive balances when encouraging cooperation.

Cooperation in public goods game does not require assortment and depends on population density.

The threshold public goods game is one of the best-known models of non-linear public goods dilemmas. Cooperators and defectors typically coexist in this game when the population is assumed to follow the so-called structured deme model. In this article, we develop a dynamical model of a general N-player game in which there is no deme structure: Individuals interact with randomly chosen neighbours and selection occurs between randomly chosen pairs of individuals. We show that in the deterministic limit, the dynamics in this model leads to the same replicator dynamics as in the structured deme model, i.e., coexistence of cooperators and defectors is typical in threshold public goods game even when the population is completely well mixed. We extend the model to study the effect of density dependence and density fluctuation on the dynamics. We show analytically and numerically that decreasing population density increases the equilibrium frequency of cooperators till the fixation of this strategy, but below a critical density cooperators abruptly disappear from the population. Our numerical investigations show that weak density fluctuations enhance cooperation, while strong fluctuations suppress it.

Effects of individual and collective decision rule on cooperation in public goods game

Research on public goods game has traditionally focused on studying the effects of punishment and reward in experimental settings, commonly known as standard games. However, these standard games often examine isolated interactions among individuals, leading to varying results based on factors such as the population studied, number of participants, and geographical context. Consequently, the understanding of cooperation evolution remains imprecise.To address this limitation, we are trying to generalize these experimental studies, we employ an agent-based model in this study to simulate interactions in public goods game and explore the influence of punishment and reward on the evolution of cooperation. Unlike standard games, evolutionary games offer a more comprehensive framework to capture and analyze a broader range of strategic interactions and behaviors.In our approach, we introduce two methods for applying punishment or reward: Individual Punishment or Reward and Collective Punishment or Reward. Under the first method, actors can individually reward or punish each other based on their contributions or free-riding behavior towards the collective good. In the second method, decisions for punishment or reward are made collectively after achieving a consensus or agreement among the members of the group. We provide a model for comparing Individual Decision Rule and Collective Decision Rule under punishment and reward, to study their effects on the evolution of contributions.Consistent with recent experimental findings, our results indicate that these mechanisms lead to a significant increase in contributions compared to the outcomes observed in standard public goods game. Additionally, we demonstrate the significant role of rewards in promoting contribution within public goods game.

The seeds of success: the pivotal role of first round cooperation in public goods games

The seeds of success: the pivotal role of first round cooperation in public goods games

Bonus-based mercenary punishment promotes cooperation in public goods games

Various regions often adopt punish strategies to solve traffic congestion problems. Punishing defectors is an effective strategy to solve the first-order free-rider problem in a public goods game. But this behavior is costly because the punisher is often also involved in the original joint venture and therefore vulnerable, which jeopardizes the effectiveness of this incentive. As an option, we could hire special players whose sole duty would be to monitor the population and punish defectors. The fines collected by various regions will also be used to subsidize the construction of public transportation. Thereby, we derive inspiration, and propose an improved public goods game model based on bonus and mercenary punishment. Research has shown that after cooperator gives the punisher an appropriate bonus, cooperators can strengthen the punisher, thereby weakening the defector's advantage and indirectly promoting cooperation by stabilizing the punisher's position in the system. In addition, the mechanism of reusing the fines collected from defectors and then subsidize to other players in the system can directly promote the emergence of cooperation.

Evolution as a result of resource flow in ecosystems: Ecological dynamics can drive evolution.

To see how the flow of energy across ecosystems can derive evolution, I introduce a framework in which individuals interact with their peers and environment to accumulate resources, and use the resources to pay for their metabolic costs, grow and reproduce. I show that two conservation principles determine the system's equilibrium state: conservation of resources- a physical principle stating that in the equilibrium, resource production and consumption should balance, and payoff equality- an economic principle, stating that the payoffs of different types in equilibrium should equal. Besides the equilibrium state, the system shows non-equilibrium fluctuations derived by the exponential growth of the individuals in which the payoff equality principle does not hold. A simple gradient-ascend dynamical mean-field equation predicts the onset of non-equilibrium fluctuations. As an example, I study the evolution of cooperation in public goods games. In both mixed and structured populations, cooperation evolves naturally in resource-poor environments but not in resource-rich environments. Population viscosity facilitates cooperation in poor environments but can be detrimental to cooperation in rich environments. In addition, cooperators and defectors show different life-history strategies: Cooperators live shorter lives and reproduce more than defectors. Both population structure and, more significantly, population viscosity reduce lifespan and life history differences between cooperators and defectors.

Evolution of cooperation in spatial public goods game based on heterogenous social preferences and dynamic punishment

The mechanism of promoting cooperation in the public goods game has always been concerned by scholars. However, most of the existing studies are based on the premise that participants are self-interested. In order to explore why some sellers on e-commerce platforms voluntarily maintain the platform’s reputation, we incorporate heterogeneous social preferences of sellers into the spatial public goods game. We find that heterogeneous social preferences can enhance cooperation by improving collective rationality. Specifically, the altruistic preference of sellers can greatly reduce free-riding behavior, while the inequality aversion preference has a little inhibitory effect. Interestingly, when the benefit of maintaining the platform’s reputation is relatively high, the reciprocal preference can inhibit cooperation, but it can promote cooperation when the benefit is relatively small. This is due to the existence of some loosely connected but stable cooperative or defective clusters of sellers in e-commerce platforms. Furthermore, we propose a dynamic punishment mechanism to punish free riders. We observe that the dynamic punishment mechanism is more effective than the static punishment mechanism in solving the second-order free-riding problem faced by punishers. Increasing the enhancement factor of public goods is identified as a fundamental approach to mitigating this problem.

Cooperation in public goods game in populations of dynamic groups with varying evolution time scales

Cooperation in public goods game in populations of dynamic groups with varying evolution time scales

Punishment credibility and cooperation in public good games

This paper investigates the efficacy of a punishment mechanism in promoting cooperative behaviour in a public goods game when punishment enforcement is risky. Experimental studies have found that a sanctioning system can induce individuals to adopt behaviour deemed socially acceptable in such games. Our experiment qualifies this result by showing that a sanctioning system can only promote cooperative behaviour if subjects perceive punishment enforcement as a high-probability event. This result supports the view that sanctioning systems can only induce people to comply with social norms that enhance efficiency if such systems are sufficiently credible. We also find that the more punishment points towards a player were not being enforced in the history of the game, the more punishment from others was directed to them. This suggests that bygones are not bygones and that punishment behaviour attempts to compensate for the history of free-riding that goes unpunished.

Zealous cooperation does not always promote cooperation in public goods games.

There is a conventional belief that prosocial behaviors cannot arise through selfish human nature, because defection always exploits cooperation to achieve a higher payoff at an individual level. Unyieldingly, some people hope to move society to cooperation through their zealous cooperation, regardless of payoffs. From the perspective of spatial evolutionary games, however, such zealous behavior is unnecessary because cooperation can emerge from selfish human nature by aggregating in evolution. Yet, to what extent can zealous cooperation induce others to cooperate? We assume a fraction of zealous agents in spatial public goods games who always cooperate. The results show that a moderate proportion of these zealous cooperators can diminish the cooperation level in the system, and cooperation is only promoted when zealots are many. Regarding spatial behaviors, the areas of zealous cooperation in a medium density can prevent evolutionary cooperation from passing through and aggregating. The phenomenon of zealous cooperation impeding cooperation becomes more pronounced when agents become less random and more selfish. This is because dotted zealous cooperation provides significant payoffs to neighboring defection, making them more solid in fitness. In this way, we also find that when zealous cooperators have low productivity, the neighbors receive fewer benefits by exploitation, thus allowing cooperation to spread. We also study replicator dynamics in unstructured populations where zealous cooperation always promotes cooperation, agreeing that zealous cooperation hindering cooperation is a spatial effect.

Bounded learning and planning in public goods games.

A previously developed agent model, based on bounded rational planning, is extended by introducing learning, with bounds on the memory of the agents. The exclusive impact of learning, especially in longer games, is investigated. Based on our results, we provide testable predictions for experiments on repeated public goods games (PGG) with synchronized actions. We observe that noise in player contributions can have a positive impact of group cooperation in PGG. We theoretically explain the experimental results on the impact of group size as well as mean per capita return (MPCR) on cooperation.

Effect of heterogeneous investment induced by payoff and emotion on cooperation in public goods games by considering memory decline effects.

Payoff, emotion, and historical memory directly determine investment decision-making for incomplete rational men in a public goods game (PGG). How these factors affect investment and cooperation behavior has not been investigated yet. Thus, we proposed a new investment model involving theses three factors to examine its coupling effect on cooperation in PGG. An emotional increment was employed to describe the emotional change in every round by supposing an investor' pleasure to a cooperator but regret to a defector. Furthermore, an emotional index was formed by accumulating these historical changes with a memory decline effect. Then an investment formula was proposed by considering this emotional index and a historical payoff. Moreover, the cooperation level affected by these factors was investigated. Results show a mutually reinforcing relationship between emotional and payoff investments. A poor memory capacity coefficient allows defectors to change their behaviors but produces some opportunists. A large memory length results in a high cooperator fraction but is not suggested to be too large.

Evolution of cooperation in public goods game in populations of dynamic groups of varying sizes

The cooperative behavior in a population engaging in Public Goods Games (PGG) with players in dynamic groups of various sizes and memberships, and a learning mechanism for switching strategy by comparing payoffs between two randomly chosen players each engaging in their own group is studied. We demonstrate that the model has the merit of allowing for an analytic treatment. Upon averaging over all possible group sizes and group constituents in PGG, we derive an analytic expression of the time evolution of the frequency of cooperation fc(t). Starting from an initial cooperative level fc(0), the population will evolve either to a 100% cooperative (AllC) or a 100% non-cooperative (AllD) state depending on the sign of a parameter K∝(r〈1/g〉−1), where r is the multiplicative factor in PGG and 〈1/g〉 is the inverse first moment of the group size distribution of players engaging in PGG. For K>0 (K<0), the system approaches an AllC (AllD) state with an exponential temporal behavior of exp(−2|K|t/M), where M is the population size. The parameter K suggests that cooperation can be promoted by suitably adjusting the multiplicative factor r to be above a critical value rc≡1/〈1/g〉. All the features predicted by the analytic results, including fc(t), the effects of the multiplicative factor r and group size distribution, and how the time constant depends on the parameter K, are confirmed by detailed numerical simulations of the model. The work sheds light on how the varying group sizes, especially the smaller groups, help promote cooperation in a PGG setting.

Panic in the Lab: The Effect of Extreme External Risks and Bolstering Cooperation in Public Goods Games

Panic in the Lab: The Effect of Extreme External Risks and Bolstering Cooperation in Public Goods Games

Ancestral social environments plus nonlinear benefits can explain cooperation in human societies

Human cooperation (paying a cost to benefit others) is puzzling from a Darwinian perspective, particularly in groups with strangers who cannot repay nor are family members. The beneficial effects of cooperation typically increase nonlinearly with the number of cooperators, e.g., increasing returns when cooperation is low and diminishing returns when cooperation is high. Such nonlinearity can allow cooperation between strangers to persist evolutionarily if a large enough proportion of the population are already cooperators. However, if a lone cooperator faces a conflict between the group’s and its own interests (a social dilemma), that raises the question of how cooperation arose in the first place. We use a mathematically tractable evolutionary model to formalise a chronological narrative that has previously only been investigated verbally: given that ancient humans interacted mostly with family members (genetic homophily), cooperation evolved first by kin selection, and then persisted in situations with nonlinear benefits as homophily declined or even if interactions with strangers became the norm. The model also predicts the coexistence of cooperators and defectors observed in the human population (polymorphism), and may explain why cooperators in behavioural experiments prefer to condition their contribution on the contributions of others (conditional cooperation in public goods games).

What drives conditional cooperation in public good games?

Extensive experimental research on public good games documents that many subjects are “conditional cooperators” in that they positively correlate their contribution with (their belief about) contributions of other subjects in their peer group. The goal of our study is to shed light on what preference and decision-making patterns drive this observed regularity. We consider reciprocity, conformity, inequality aversion and residual factors, such as confusion and anchoring, as potential explanations. Effects of these drivers are separated by varying how others’ contributions are determined and the informational content of the conditioning variable across treatments. Assuming additive separability of the effects of the four drivers, we find that, of the average conditionally cooperative behavior, at least 40 percent is driven by residual factors. For the remainder, most is accounted for by inequality aversion, some by conformity and very little by reciprocity. These findings carry an important message for how to interpret conditional cooperation observed in the lab. We also discuss what these findings mean for understanding conditional cooperation in fundraising applications in the field.

The Strategy Method Risks Conflating Confusion with a Social Preference for Conditional Cooperation in Public Goods Games

The strategy method is often used in public goods games to measure an individual’s willingness to cooperate depending on the level of cooperation by their groupmates (conditional cooperation). However, while the strategy method is informative, it risks conflating confusion with a desire for fair outcomes, and its presentation may risk inducing elevated levels of conditional cooperation. This problem was highlighted by two previous studies which found that the strategy method could also detect equivalent levels of cooperation even among those grouped with computerized groupmates, indicative of confusion or irrational responses. However, these studies did not use large samples (n = 40 or 72) and only made participants complete the strategy method one time, with computerized groupmates, preventing within-participant comparisons. Here, in contrast, 845 participants completed the strategy method two times, once with human and once with computerized groupmates. Our research aims were twofold: (1) to check the robustness of previous results with a large sample under various presentation conditions; and (2) to use a within-participant design to categorize participants according to how they behaved across the two scenarios. Ideally, a clean and reliable measure of conditional cooperation would find participants conditionally cooperating with humans and not cooperating with computers. Worryingly, only 7% of participants met this criterion. Overall, 83% of participants cooperated with the computers, and the mean contributions towards computers were 89% as large as those towards humans. These results, robust to the various presentation and order effects, pose serious concerns for the measurement of social preferences and question the idea that human cooperation is motivated by a concern for equal outcomes.

Persistent imitation paves the way for cooperation in public goods game

In previous studies of evolutionary games, players change reference objects at each time step. However, in real life, many people tend to consistently imitate outstanding role models instead of changing reference objects frequently. From this, a persistent imitation rule is proposed. In detail, a persistent imitator will persist in imitating his or her reference object until the wealth exceeds that of the reference object or the duration of continuous imitation exceeds a specific value. Furthermore, to reflect inter-individual differences, we divide the players into two categories, persistent imitators and random imitators. The simulation suggests that the presence of a high proportion of persistent imitators has a significant effect on the development of cooperation, and the level of cooperation increases as the maximum duration of imitation increases. However, when the proportion of persistent imitators or the maximum duration of imitation is small, the promotion effect on cooperation is not obvious.

The interplay between reputation and heterogeneous investment enhances cooperation in spatial public goods game

In previous studies about heterogeneous investment, many researchers only focus on the monodirectional effect of reputation, but ignore the reversed influence about the heterogeneity of reputation fluctuation driven by investment. Given this, considering the interplay between reputation and heterogeneous investment, we explore the evolution of cooperation in public goods game. In detail, each player's reputation situations in different groups determine its differentiated investment amounts, and in turn, the heterogeneity of reputation fluctuation is dependent on how much it invests into each group. Furthermore, we introduce two parameters, α and β, to characterize the effect degree of investment on heterogeneous reputation fluctuation and the one of reputation on heterogeneous investment, respectively. The simulation results suggest that cooperation can be boosted to some extent, especially for the larger α and β, as they magnify the interplay of reputation and heterogeneous investment.

Evolution of cooperation in public goods games with segregated networks and periodic invasion

Despite the cost, rational individuals routinely modify their relationships in social networks to optimize their payoffs. To develop this observation, we propose a segregation strategy that impels individuals to sever the adverse ties between defectors and their group at some cost, and then we randomly rewire the link-broken cooperative individuals. Moreover, time-varying environmental factors impact the relationships between interacting individuals, in particular certain periodic changes such as the circadian rhythm and seasonality, thus affecting the evolution of cooperation in spatial public goods games. By this means, periodic invasion is taken into account, which allows defectors with lower degrees than the initial value to randomly restore links and invade the population again. Through simulation, we find that the segregation strategy involving periodic invasion can effectively facilitate cooperation by formatting assortative and heterogeneous topology. Furthermore, we observe a subtle interplay between the costly topology control strategy and the exogenous changes in temporal factors that alter the spatiotemporal dynamics of coevolution and promote cooperation. We conclude that a relatively low periodic invasion frequency contributes to increasing the level of cooperation, but the threshold of cooperation is not sensitive to the change in invasion period when at longer intervals. We present our interpretations of these phenomena, which thus allow us to better understand the role of this new machine in the emergence of cooperation.