Threshold Public Goods Game Research Articles

Free-rider or contributor: A dilemma in spatial threshold public goods games

Late movers refer to individuals who adjust their strategies after observing the choices of others in a public goods game, can significantly impact the likelihood of public goods provision. This creates a social dilemma: late movers act as free-riders to rely on others to contribute, yet they also risk the public good not being provided if contributions fall short. To address this dilemma, we utilize a spatial threshold public goods game model to examine how the behaviors of late movers influence overall cooperative levels within a population. We propose a probabilistic rule for late movers that captures the dilemma between cooperating to enhance the collective good and free-riding to maximize individual benefits. Our findings indicate that strategic late movers can significantly enhance cooperation by adapting to local cooperation levels. However, an excessively high proportion of late movers may reduce the overall level of cooperation. Additionally, the formation of clusters by late movers results in higher cooperative levels compared to random distribution. Our study provides novel insights into the dynamics of cooperation within the framework of spatial threshold public goods games. By incorporating the role of late movers, we highlight how adaptive strategies can mitigate the free-rider problem and promote cooperative behaviors.

Children Sustain Cooperation in a Threshold Public-Goods Game Even When Seeing Others’ Outcomes

Many societal challenges are threshold dilemmas requiring people to cooperate to reach a threshold before group benefits can be reaped. Yet receiving feedback about others’ outcomes relative to one’s own (relative feedback) can undermine cooperation by focusing group members’ attention on outperforming each other. We investigated the impact of relative feedback compared to individual feedback (only seeing one’s own outcome) on cooperation in children from Germany and India (6- to 10-year-olds, N = 240). Using a threshold public-goods game with real water as a resource, we show that, although feedback had an effect, most groups sustained cooperation at high levels in both feedback conditions until the end of the game. Analyses of children’s communication (14,374 codable utterances) revealed more references to social comparisons and more verbal efforts to coordinate in the relative-feedback condition. Thresholds can mitigate the most adverse effects of social comparisons by focusing attention on a common goal.

Carbon Pricing, Carbon Dividends and Cooperation: Experimental Evidence

We investigated whether carbon taxes with and without carbon dividends improve cooperative behavior to mitigate simulated climate change. We implemented a randomized controlled trial on a large sample of the U.S. general population (N=2,116). Played in real-time in groups of four, we tested three carbon-pricing treatments and a baseline condition within a modified threshold public goods game of loss avoidance. We found that a carbon tax coupled with carbon dividends reduces carbon-emitting group consumption relative to a baseline condition with no tax, and relative to a carbon tax only. A carbon tax coupled with carbon dividends paid out to below-average polluters (asymmetric dividend) worked best, with 94% of groups remaining below a critical consumption (emission) threshold. We also found that experiencing the asymmetric dividend condition positively affected perceptions of carbon pricing with carbon dividends.

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.

Cooperation dynamics in public goods games with evolving cognitive bias

It has been proved that cognitive biases widely exist in various social realities and lead to unprecedented consequences by affecting individual judgment and decision-making processes in distinct ways. To further explore the influence of changeable cognitive bias, we introduce a heterogeneous population and learning process that can be influenced by cognitive bias into the threshold public goods game (TPGG). Specifically, additional parameters describing the heterogeneity and updating speed of bias are employed. The combined effects of bias and the inherent parameters in the TPGG model on the evolution of cooperation are explored. Numerical simulation results show that the heterogeneity of cognitive bias exhibits diametrically opposite effects when the threshold is relatively low and high, and the effect of incentives based on fixed reward and adjustable punishment are distorted by heterogeneous cognitive biases as well. In addition, the process of social learning forces individuals to update their beliefs toward the direction of obtaining a higher payoff. Different learning rates eventually lead to distinct levels of cooperation by changing the distribution of cognitive bias when the population reaches the evolutionary steady state. Our work extends the research framework on cognitive bias from the perspective of population heterogeneity and explores the impact of individuals' learning ability on personal bias and cooperative behavior.

Cooperation and Coordination in Threshold Public Goods Games with Asymmetric Players

In this paper, we study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments ei, productivities pi, and rewards ri. In general, this game has a defective Nash equilibrium (NE), in which no one contributes, and multiple cooperative NEs, in which the group’s collective contribution equals the threshold. We then study how multiple dimensions of inequality influence people’s cooperation and coordination. We show that heterogeneity in eipi can promote cooperation in the sense that the existence condition of the defective NE becomes stricter. Furthermore, players with higher eipi are likely to contribute more at a cooperative NE in terms of collective contribution (i.e., absolute contribution multiplied by productivity).

Paying for agricultural information in Malawi: The role of soil heterogeneity

We examine the relationship between soil heterogeneity and investment in learning among farmers in Malawi using an experimental approach. Soil heterogeneity may both impede social learning and encourage experimentation. In our experiment, farmers contribute towards the purchase of a single soil test in the village in a threshold public goods game. This soil test provides farmers with valuable and actionable information. By randomly varying the plot selected for soil testing we establish the role of soil heterogeneity. We find that farmers contribute more when they perceive soils to be more similar to their own plot, but also free ride on others whose soils they perceive as similar. This free riding increases in larger groups of farmers with similar soils. Despite this, all villages consistently contribute enough to purchase the soil test.

Can collective conditionality improve agri-environmental contracts? From lab to field experiments

Individual subsidy payments that are conditional on a collective contribution threshold could provide a viable resolution to the insufficient and dispersed adoption of agri-environmental contracts aiming at attaining environmental quality targets. Indeed, in a decontextualized laboratory experiment based on a threshold public goods game (TPGG), Le Coent et al. (2014) offer promising results regarding a conditional subsidy compared to an unconditional subsidy (i.e., the standard subsidy in existing agri-environmental schemes). In this article, we propose to improve the external validity of these results by transposing this laboratory experiment to a lab-in-the-field setting with farmers. To do so, we carry out a contextualized lab-in-the-field experiment with farmers by explicitly mentioning agri-environmental contracts and water quality. Our results show that farmers cooperate even more successfully than students and sustain more efficient outcomes over time. In a between-subject comparison, our results indicate that average group contributions under the conditional and the unconditional subsidy mechanisms are not significantly different. We find that this is due to two behavioral responses (perceived risks and initial beliefs on others’ contributions) in the conditional subsidy treatment, which show to have opposing effects on contributions that cancel each other out. The conditional incentive mechanism thus shows promising potential as a tool for agri-environmental policy since it avoids the pay-for-nothing trap of the unconditional subsidy mechanism without discouraging contributions.

Avoiding the Climate Catastrophe: Heterogeneous Abatement Costs and Voting on Redistribution in a Threshold Public Good Game

Avoiding the Climate Catastrophe: Heterogeneous Abatement Costs and Voting on Redistribution in a Threshold Public Good Game

Assurance payments on the coordination of threshold public goods provision: An experimental investigation

AbstractWe investigate the assurance payment mechanism (APM) in a single‐unit threshold public good game. APM offers an assurance payment () as compensation to would‐be contributors if the group fails to provide the good and individual contributions reach a pre‐determined price. We characterize the set of pure‐strategy Nash equilibria for APM under complete information and show that assurance payments substantially reduce the multiplicity of equilibria and eliminate the set of non‐provision equilibria in a general setup. We find strong evidence that APM improves upon the baseline provision point mechanism without assurance in lab experiments. Assurance payments act as a coordination device and induce more contributions concentrated on , especially for agents with values above , leading to more frequent successful provision, higher group contributions, and an overall welfare improvement. Our experimental findings highlight the non‐equilibrium mis‐coordination as the main reason for the non‐provision of threshold public goods and indicate that the format of assurance payments plays a key role in successful coordination even when provision is the unique equilibrium outcome.

I’m not sure what to think about them: Confronting naive present bias in a dynamic threshold public goods game

This paper explores the implications of naive present bias in a simple, dynamic threshold public goods game. Our analysis demonstrates how equilibrium behavior and outcomes can be highly dependent on the “direction” with which players reassess their naive prior beliefs (including higher-order beliefs) regarding both players’ present biases. In some situations, a naive player may actually become more inclined to exert effort in pursuit of a future reward upon discovering their own present bias.

Common knowledge promotes cooperation in the threshold public goods game by reducing uncertainty

Recent work suggests that an important cognitive mechanism promoting coordination is common knowledge—a heuristic for representing recursive mental states. Yet, we know little about how common knowledge promotes coordination. We propose that common knowledge increases coordination by reducing uncertainty about others' cooperative behavior. We examine how common knowledge increases cooperation in the context of a threshold public goods game, a public good game in which a minimum level of contribution—a threshold—is required. Across three preregistered studies (N = 5580), we explored how varying (1) the information participants had regarding what their group members knew about the threshold and (2) the threshold level affected contributions. We found that participants were more likely to contribute to the public good when there was common knowledge of the threshold than private knowledge. Participants' predictions about the number of group members contributing to the public good and their certainty ratings of those predictions mediated the effect of information condition on contributions. Our results suggest that common knowledge of the threshold increases public good contributions by reducing uncertainty around other people's cooperative behavior. These findings point to the influential role of common knowledge in helping to solve large-scale cooperation problems.

Would community conservation initiatives benefit from external financial oversight? A framed field experiment in Namibia’s communal conservancies

It is commonly asserted that the successful management of common property resources (CPR), and by extension, the provision of public goods such as biodiversity and carbon, requires the devolution of control to local communities. However, where trust in community institutions is low, the intrinsic motivation to co-operate may be diminished. In this study, we carried out surveys and framed field experiments on the introduction of payments for ecosystem services (PES) to Namibia’s communal conservancies, established under the community-based natural resource management (CBNRM) programme. We used a threshold public good game where income from conservation efforts would require cooperation in terms of investing in conservation management and thereby also sacrificing opportunities to use designated wildlife areas. Our study found that households had low confidence in the conservancy management institutions and were more willing to co-operate when external financial oversight was provided. In fact, addressing the risk of financial mismanagement was more important than the payment level. Participants with a low level of confidence in the conservancy management contributed significantly less, but the gap narrowed when oversight was introduced. This suggests that initiatives to incentivise conservation of communally-owned land may require the close involvement of trustworthy external organisations to ensure their effectiveness.

Cooperation against all predictions

AbstractIn Binary Threshold Public Good (BTPG) games, n players have binary choices: cooperation or non‐cooperation. If at least k players cooperate, a public good is produced. The case k = n is the Stag Hunt game with the two pure strategy equilibria E1 (all players cooperate) and E0 (no player cooperates). In four rather diverse examples of four‐player Stag Hunt games, three prominent concepts of equilibrium selection favor E0. Experiments, however, result in cooperation frequencies between 70.3% and 99.7%. Also for k < n, the selected equilibria clearly differ from experimental behavior. We interpret our observations by suggesting the concept Behavioral Equilibrium Selection.

Communication in a threshold public goods game under ambiguity

ABSTRACT This paper offers evidence on the impact of communication on the provision of public goods whose quality is uncertain, such as investment in prevention or fundraising in favour of non-governmental organizations (NGO). We run a laboratory experiment with two treatments, where the control variable is pre-play communication via unrestricted text chat. A binary threshold public goods game with four-person groups, threshold of three contributors and provision mechanism with elements of ambiguity is at the core of the design. A private signal linked to the real value of the public good supports the contribution decision. We find that unexpected low-valued public goods can undermine future willingness to contribute, although the benefits of communication still prevail in the form of higher public good provision. We also detect unprecedented inefficiency coming from overcontribution, given that subjects tend to neglect the free-rider problem. Chat analysis reveals that players favour the minimization of ambiguity over the maximization of the group earnings, so that we finally speculate that under uncertainty satisficing is more salient than optimizing.

Endogenous Shared Punishment Model in Threshold Public Goods Games

Population growth and greater human well-being imply increased use of scarce resources, which makes innovative proposals for fair redistribution policies necessary. The utilisation of common-pool resources (CPRs) offers an economising solution to this problem; however, addressing the complex issue of harmonising the participants’ interests is challenging. The use of CPRs has been theoretically discussed for decades and is addressed by theory of public goods (PGs) provision. Surprisingly, experimental tests of this theory have observed systematic deviations from the theoretical conclusions. Economists have applied agent-based methods to resolve this puzzle. We follow this approach and propose an agent-based model that innovatively employs voting on the punishment of free/cheap riders. The voting participants simultaneously determine the strictness of the punishment meted out to free/cheap riders and the cost burden of this punishment system. The proposed endogenous shared punishment model works within the threshold public goods game framework. Simulation results show that the presented method is more efficient than models with full or no punishment. Furthermore, the involvement of activists increases the likelihood of PGs provision. Introducing voting into PGs provision increases its efficiency and thus extends the set of available solutions to increase the efficiency of PGs provision.

Evolutionary dynamics in spatial threshold public goods game with the asymmetric return rate mechanism

In reality, cooperators often are provided a higher return rate for their contributions. Inspired by the reality, this paper introduces the asymmetric return rate mechanism, where the return rate is asymmetric between cooperators and defectors. This paper mainly studies how the asymmetric return rate mechanism influences the evolutionary dynamics in spatial threshold public goods game on two different complex networks, the namely square lattice and Barabási-Albert scale-free network. The simulation results show that increasing the sensitivity for the spread of cooperation is more effective than increasing that for the spread of defection not only to promote cooperation, but also to elevate the provision of the public goods. In addition, a moderate value of threshold is the best to elevate both the promotion of cooperation and the provision of the public goods.

High thresholds encouraging the evolution of cooperation in threshold public-good games

For a well-mixed population, we consider a threshold public good game where group members only obtain benefits from a public good if a sufficiently large number of them cooperates. We investigate the effect of an increase in the threshold on the level of cooperation that evolves. It is shown that for sufficiently large participation costs, the level of cooperation is higher for low and for high thresholds, than it is for intermediate thresholds – where in the latter case cooperation may not evolve at all. The counterintuitive effect where an increase in the threshold from an intermediate to a high one decreases the probability of cooperation, is related to the so-called common-enemy hypothesis of the evolution of cooperation. We further apply our analysis to assess the relative weight of different game types across the parameter space, and show that game types where either a small, or a large fraction of the population evolves as cooperators, receive more weight compared to game types where an intermediate fraction of cooperators evolves.

Multiple learning mechanisms promote cooperation in public goods games with project selection

How evolution favors cooperation is a fundamental issue in social and economic systems. In the business world, actively selecting a suitable project is usually helpful for a businessman to be in an advantageous position. By incorporating project selection mechanism into the threshold public goods game, we have investigated the coupling effect of mutation and imitation in updating one's preferred project scale on the evolution of cooperation. Compared with the situation where there is no project selection mechanism, the existence of project selection may suppress or promote cooperation depending upon different updating rules. There exists a critical ratio of the imitators in the population, below which cooperation is suppressed while above which cooperation is promoted. With the coevolving of individual strategies and preferred project scales, a higher level of cooperation corresponds to a larger average value of the preferred project scales. A theoretical analysis indicates that, as most of the individuals are mutants, the coevolving process is governed by the mutation process, which leads to a smaller average value of the preferred project scales and a lower level of cooperation. As most of the individuals are imitators, the coevolving process is governed by the coupling of the mutation and imitation processes, which leads to a larger average value of the preferred project scales and a higher level of cooperation. As all the individuals are imitators, the coevolving process is governed by the imitation process, which leads to an intermediate average value of the preferred project scales and an intermediate level of cooperation.

Analysing group contract design using a threshold public goods experiment

AbstractThis paper presents the results of a threshold public goods game experiment with heterogeneous players. The experiment is designed in close collaboration with the Dutch association of agri-environmental farmer collectives. Subjects are recruited at a university (study 1) and a farm management training centre (study 2), the subjects of the second study most resembling the subjects in the field. The experiment consists of several treatments and each treatment has two different distribution rules, which are varied in a within-subjects manner. After subjects have experienced both, they can vote for one of the two rules: either a differentiated bonus that results in equal payoff for all, or an undifferentiated, equal share of the group bonus. In a between-subjects manner, subjects can vote for a (minimum or average) threshold or are faced with an exogenous threshold. The results indicate that exogenous thresholds perform better, possibly because the focal point they provide facilitates coordination. With regard to the two distribution rules, the results are mixed: in study 1, average contributions and payoffs are higher under the ‘equal-payoff’ rule, but there is no significant difference between the two in study 2. Overall, our results suggest that environmental payment schemes should consider cost heterogeneity in the design of group contracts, and pay explicit attention to coordination problems too.