Linear Public Goods Game Research Articles

Heterogeneous productivity stabilizes public good contributions under certainty, uncertainty and ambiguity

Typically, a linear public goods game with a voluntary contribution mechanism (VCM) sees declining contributions over repeated one-shot periods of play. However, contributions under uncertainty or ambiguity over heterogeneous productivity on individual contributions have yet to be investigated. We compare contributions under homogenous productivity of 0.6; and certain, uncertain (for future periods only and all periods) or ambiguous heterogeneity in productivity, which can be either a high (0.9) or a low (0.3) type. Certain heterogeneity unexpectedly stabilizes contributions over homogenous, led by high productivity types. Uncertain or ambiguous heterogeneity in productivity weakly lowers contributions, but they remain stable. Thus, in a novel finding that is replicated across our treatments, heterogeneous productivity appears to support stable contributions over time, even when productivity is unknown at time of contribution. This finding suggests uncertain and heterogeneous productivity are an important characteristic of public goods that needs to be considered when modelling them in the field, and reinforces the role of productivity itself in driving voluntary public good contributions.

Cognitive ability and the house money effect in public goods games

AbstractI experimentally investigate the relation of endowment origin, cognitive abilities (as measured by the Cognitive Reflection Test, CRT), and co-operation in a one-shot linear public goods game. The results show that subjects’ contributions depend on an interplay of cognitive abilities and endowment origin. A house money effect exists only for subjects with low CRT scores. They contribute more when income was allocated to them and less when income was obtained by effort. In contrast, subjects with high CRT scores contribute the same amount independent of income type. The findings have implications for redistribution, team production, and experimental designs.

Variance, norms and cooperative behavior in public goods games.

This study examines the relationship between the variance of others' contributions, social norms (empirical and normative expectations), and cooperative behavior using a classic linear public goods game. The following results are observed. First, the variance of a participant's group members' contributions had a negative impact on their contributions, empirical expectations, and normative expectations. Second, deviations from the mean, whether negative or positive, were deemed less socially appropriate. Third, while there was a strong relationship between variance, social norms, and cooperative behavior, the mediating effect of social norms was found to be insignificant. Finally, there were some notable findings regarding behavior type. Although free riders and cooperators exhibited distinct behavioral patterns, their normative expectations were similar. Free riders expected others to cooperate, but their empirical expectations were significantly lower than cooperators' expectations, which were aligned with their actual contributions. These findings contribute to research on the relationship between distribution heterogeneity, social norms and cooperative behavior. Furthermore, these findings provide valuable insights into management practices.

Cooperation and confusion in public goods games: confusion cannot explain contribution patterns

People behave much more cooperatively than predicted by the self-interest hypothesis in social dilemmas such as public goods games. Some studies have suggested that many decision makers cooperate not because of genuine cooperative preferences but because they are confused about the incentive structure of the game—and therefore might not be aware of the dominant strategy. In this research, we experimentally manipulate whether decision makers receive explicit information about which strategies maximize individual income and group income or not. Our data reveal no statistically significant effects of the treatment variation, neither on elicited contribution preferences nor on unconditional contributions and beliefs in a repeated linear public goods game. We conclude that it is unlikely that confusion about optimal strategies explains the widely observed cooperation patterns in social dilemmas such as public goods games.

Accounting for preferences and beliefs in social framing effects

Past experiments show systematic differences in contributions to public goods under various framing conditions. Several explanations of these differences have been presented. Some suggest that social frames affect subjects' preferences, while others suggest that framing changes subjects' beliefs about others, and thus in turn affects behavior. In this paper, we test the effect of framing on the level of contributions in a series of public goods games designed to separate the impact of preferences from beliefs in shaping cooperative decisions. This is achieved by implementing a social value orientation measure to elicit social preferences from decision makers, which are then analyzed in concert with reported beliefs about others' cooperation and own contribution decisions from the linear public goods games. While we find mixed results on framing effects, our study demonstrates that preferences and beliefs are significant predictors of cooperation. Furthermore, the degree to which they influence cooperation is either strengthened or weakened by framing.

Expertise, Social Influence, and Knowledge Aggregation in Distributed Information Processing.

In many social, cyber-physical, and socio-technical systems, a group of autonomous peers can encounter a knowledge aggregation problem, requiring them to organise themselves, without a centralised authority, as a distributed information processing unit (DIP). In this article, we specify and implement a new algorithm for knowledge aggregation based on Nowak's psychological theory Regulatory Theory of Social Influence (RTSI). This theory posits that social influence consists of not only sources trying to influence targets, but also targets seeking sources by whom to be influenced and learning what processing rules those sources are using. A multi-agent simulator SMARTSIS is implemented to evaluate the algorithm, using as its base scenario a linear public goods game where the DIP's decision is a qualitative question of distributive justice. In a series of experiments examining the emergence of expertise, we show how RTSI enhances the effectiveness of the multi-agent DIP as a social group while conserving each agent's individual resources. Additionally, we identify eight criteria for evaluating the DIP unit's performance, consisting of four conflicting pairs of systemic drivers, and discuss how RTSI maintains a balanced tension between the four driver pairs through the emergence and divergence of expertise. We conclude by arguing that this shows how psychological theories like RTSI can have a crucial role in informing agent-based models of human behaviour, which in turn may be critically important for effective knowledge management and reflective self-improvement in both cyber-physical and socio-technical systems.

Bringing tax avoiders to light: moral framing and shaming in a public goods experiment

AbstractWith a linear public goods game played in six different variants, this article studies two channels that might moderate social dilemmas and increase cooperation without using pecuniary incentives: moral framing and shaming. We find that cooperation is increased when noncontributing to a public good is framed as morally debatable and socially harmful tax avoidance, while the mere description of a tax context has no effect. However, without social sanctions in place, cooperation quickly deteriorates due to social contagion. We find ‘shaming’ free-riders by disclosing their misdemeanor to act as a strong social sanction, irrespective of the context in which it is applied. Moralizing tax avoidance significantly reinforces shaming, compared with a simple tax context.

The impact of smiling cues on social cooperation

AbstractWhile there is a plethora of experimental studies on the effects of preplay communication on economic behavior, little is known about the impact of simple cues, such as smiling, on pro‐sociality. This article presents a comprehensive analysis exploring how the presence of a smiling opportunity affects pro‐social behavior as measured by a one‐shot linear public goods game. Our design varies (i) whether smiling is costly or costless and (ii) whether one or both members in a group are given the opportunity to smile. To test for the robustness of our results, we consider two versions of smiling cues: (i) a smiling label and (ii) a smiling face (emoji). Our findings indicate that introducing a cost for smiling has detrimental behavioral consequences regardless of the cue. Specifically, when smiling is costly, only a small minority of subjects are willing to smile as opposed to when smiling is costless. As a result, subjects contribute significantly less. These results remain the same regardless of the type of smiling cue that subjects can send. Overall, our findings provide new evidence that simple cues such as smiles embody information that influences pro‐social behavior in social interactions.

Reciprocity in Dictator Games: An Experimental Study

When decisions are made before roles are assigned, the Dictator Game is strategically equivalent to a linear Public Goods Game. This suggests that, when played between individuals with the same income, the prosocial behavior observed may be attributed at least in part to reciprocal altruism. Dictators transfer money only because they believe Recipients would transfer money as well, if roles were reversed. By contrast, when the game is played between individuals with different background income, the generosity of the rich towards the poor is more easily attributed to pure, non-reciprocal altruism. We test this hypothesis by eliciting conditional preferences for giving in a Dictator Game in two treatments. In the first students are matched with other students, while in the second students are matched with subjects living in a refugee camp in Uganda. We find that our predictions are only partially borne out by the data. Whether giving is directed to a person with similar or lower socioeconomic status, most subjects reveal conditionally altruistic preferences. Unconditional altruism is virtually absent in both treatments. These counter-intuitive results have important implications for the experimental elicitation of social preferences.

Cooperation under social and strategic uncertainty – The role of risk and social capital in rural Cambodia

Cooperation in a social dilemma is noble but risky because one is not sheltered against selfish individuals. This “social uncertainty” is essentially captured in the linear public good game, where it is socially optimal to contribute everything to the public good, while it is privately optimal to keep everything for oneself. Many real-world social dilemmas have an additional source of “strategic uncertainty”, as socially and privately optimal strategies tend to depend on actions of others. Here, we compare the determinants of cooperation in a linear public good game and a threshold game, where individuals are challenged to guess the contributions of the partners to determine an appropriate investment that aligns with private and collective interest. We combine elicited risk preferences and cooperative attitudes with information from a survey on social capital and demographics to analyse what explains cooperation. Our experiments are carried out with farmers in Cambodia who are exposed to various social dilemmas on a daily basis. We find that risk and social capital explain cooperation in the linear public good game, but not in the threshold game. These findings call for a more careful examination of real world social dilemmas that typically comprise coordination and cooperation elements.

Sharing and cooperation in an experiment with heterogeneous groups

We investigate the impact of inequality on sharing and cooperation using a dictator game and a linear public good game where some participants work for their endowment (“workers”) while others do not (“non-workers”). Moreover, we differentiate between two types of inequality, namely in source and in level. In contrast to most studies, participants are fully informed about the endowment of the other players. The key finding of our paper is that both sharing and cooperation critically depend on the source of the endowment. In particular, workers are more likely to share with other workers than with non-workers and more inclined to contribute to the public good when grouped with other workers rather than when grouped with non-workers. Considering also the choices made by non-workers, we argue that the worker premium in sharing and cooperation is based on fairness considerations rather than an in-group bias. Adding inequality in the level of endowment reduces the importance of the source of endowment as driver of behavior. This also suggests that reducing one layer of inequality may not improve cooperative behavior in society significantly, implying that a big-push policy tackling many dimensions of inequality at the same time may be required.

Individuele verschillen in sociale dilemma’s

Summary Individual differences in social dilemmas: the effect of trust on costly punishment in a public goods gameThe establishment of cooperation in public goods dilemmas is important to real life problems such as improving the environment. Cooperation is facilitated when people are able to punish uncooperative behavior. Individual characteristics of persons, however, can affect cooperation and punishment behaviour. This study focuses on individual differences in trust and investigates the effect of trust on cooperation and punishment behaviour in a linear public goods game with peer punishment opportunities. The research question is: ‘What is the effect of individual differences in trust on cooperation and on the likelihood of punishing non-cooperative behaviour of fellow players in public goods games with punishing possibilities?’ Experimental data of 148 participants is used to research their cooperation and punishment behaviour. Multilevel regression is used to analyse the data. The results demonstrate a positive effect of trust on cooperation. We do not find an effect of trust on punishment. Further suggestions are provided for future research on how individual motivations still might affect behaviour in a social dilemma with punishment opportunities.

Coordination and Free-Riding Problems in Blood Donations

This article theoretically and experimentally examines the twin problems of free-riding and coordination failure faced by blood banks, by investigating the effects of information provision on the efficiency of blood donation. We augment a standard linear public goods game, incorporating the following features of blood donation: multiplicity of public goods (to reflect intertemporal coordination issues), current and upcoming upper bound demands (to incorporate the perishable nature of blood and the embargo period of consecutive donations), and semi-binary choices (to account for individual options to withhold donations or make donations and when). We analyze whether a provision of deterministic information on the potential blood demand (full information) would improve the efficiency of blood when compared to the provision of probabilistic information (partial information). The theory predicts that if each individual maximizes the payoff-sum of all players, then the full information provision would achieve efficiency in equilibrium. The results of laboratory experiment show that the full information provision does not improve the efficiency of donation, on an average. We find that full information improves intertemporal coordination, but it worsens the free-riding problem. Although information helps individuals to direct donations in response to the demand, it drives individuals to withhold donations to avoid potential wastage against the risk of over the upper bound. When the predicted total demand is relatively small, that is, when strategic uncertainty about others’ matters for achieving efficiency, the provision of information about intertemporal demand in upper bounds tends to lower efficiency because the donation withholding'' effect becomes dominant.

The effects of voice with(out) punishment: Public goods provision and rule compliance

We investigate the effect of voice exercised through comment-based participation on individual public goods provision. We implement a modified linear public goods game with treatments along two dimensions. First, we introduce a comment mechanism where individuals can provide unstructured feedback to influence a third-party rule-maker who determines a minimum contribution rule (MCR) at the beginning of the game. Second, we implement a probabilistic sanctioning mechanism for individuals who do not contribute at least the MCR. We find that without punishment, comments are insufficient to maintain high contribution levels over time. However, when enforcement is present, comment-based participation has a positive effect on players’ contributions to the public good and on their probability of compliance with the MCR. Comments also have a large positive effect on the MCR set by the rule-maker; players, in turn, respond to an increase in the MCR by making larger contributions to the public good.

Social value orientation and group size uncertainty in public good dilemmas

Risk and uncertainty are an integral part of everyday human interactions. Recent literature has shown that group size uncertainty might change strategic cooperation behavior in significant ways. In this paper, we investigate how conditional cooperation changes under group size uncertainty in a linear public good game where the selfish rational strategy is kept constant. Further, we suggest an underlying mechanism that consists of beliefs and group size estimation. We show that interpersonal differences (i.e., Social Value Orientation) are essential in how this mechanism operates. More specifically, we find that prosocials contribute more under uncertainty compared to certainty, whereas proselfs do not change their behavior. Given the same feedback proselfs estimated the group size to be bigger than prosocials, resulting in a smaller contribution belief. These results imply that interpersonal differences are important in explaining cooperation under uncertainty compared to certainty.

Cooperation and Competition in Public-Sector Negotiations: A Laboratory Experiment

Negotiating is a core activity in the public and private sector. Because of varying public service motivation (PSM) between public- and private-sector employees, we expect them to behave differently in negotiations. Moreover, one-shot negotiation settings are often studied even as many real-world negotiations are repeated exchanges. We apply a repeated linear public goods game in a laboratory experiment to test the link between PSM and the level of cooperation by using a sample of graduate and undergraduate students. The results show that high-PSM participants, indeed, contributed more over the entire experiment, and therefore, acted more cooperatively in a repeated negotiation. Matching negotiators to opponents with high-PSM, low-PSM did not alter the level of cooperation in negotiation. Based on this, we conclude that cooperation in repeated negotiations is not conditional on the PSM of opponents. We conclude with implications for theory and practice.

Voluntary contributions of time: Time-based incentives in a linear public goods game

This paper presents the findings of an experimental study designed to investigate whether the pattern of contributions elicited in a Voluntary Contribution Mechanism (VCM) replicates the stylized facts reported in the literature when participants’ time, rather than their money, is at stake. In this experiment, participants are all confronted to the same incentive structure. For half of them, the game is materialized using monetary payoffs, as is done in standard VCM studies. For the other half, the returns from the private and public accounts are implemented as reductions in waiting time. Experimental procedures are designed to keep the decision domain, the size of incentives and the degree of confidentiality constant across the two resources. The contribution patterns elicited by both treatments are found to be (i) remarkably similar and (ii) in line with the picture typically drawn in the literature. Group contributions are statistically indistinguishable in terms of average, variability and distribution, in virtually all rounds of the game. Although I do find a significant difference in the decay rate of contributions across rounds, seemingly driven by a greater proportion of early free-riders and late full contributors in the Time Treatment, this effect is both small in magnitude and inconsequential in terms of game efficiency. Overall, the stylized facts often presented in the VCM literature seem to be robust to a change in operationalization of the incentive structure.

Free-rider Problem in Classroom Games - Impact of Gender and Intergroup Conditions

Behavioural experiments in the field of provision of public goods (including free rider problem) help to uncover the underlying processes and forces determining the nature of economy in the public sector. The objective of this paper is to determine the impact of gender and intergroup conditions on the extent of cooperation in standard linear public goods game using the voluntary contribution mechanism. Design of the teaching experiment is based on the methodology of Špalek (2011) with some modification. There were 80 undergraduate students of business participating in the classroom game, age range 20–22 years. Students were divided into three independent groups by 26 to 27 participants. Each group was playing independently, and individual strategies were recorded. We used the nonparametric tests (Mann‑Whitney U test and Kruskal‑Wallis Test) to analyse the differences between the gender and groups. Findings do not show statistically significant difference based on gender. On the other hand, the intergroup conditions determined by the social dynamics and discussion have significant influence on the distribution of goods. Results bring strong evidence on the importance of social and political factors influencing the pro‑social behaviour in the society.

Positive framing does not solve the tragedy of the commons

We investigate whether positive framing increases cooperation in three social dilemmas with slightly different properties: a linear public goods (PG) game, a non-linear PG game, and a common pool resource (CPR) game. Results from our laboratory experiments show that contributions to a linear PG are higher if the externality is framed positively, rather than negatively, corroborating earlier findings by Andreoni (1995). By contrast, we find no such framing effects in the non-linear PG game or the CPR game. In these games, the best response in the material payoffs is to contribute less if others contribute more, counteracting effects of pro-social preferences. Positive framing therefore does not help to solve the tragedy of the commons.

Belief Heterogeneity and the Restart Effect in a Public Goods Game

We explore how subjects with heterogeneous beliefs respond to a surprise restart in a linear public goods game played for 20 rounds using either a “partners” or a “strangers” protocol. There are two restarts: one prior to Round 11 and another prior to Round 16. We elicit subject beliefs at the outset and classify subjects into three groups—Top, Middle, and Bottom—depending on their prior beliefs about their peers’ contributions to the public good. Then, we look at how these three groups respond, in terms of their beliefs and contributions, before and after the restart. We replicate the restart effect, but find that (i) it is much more pronounced for partner matching than for stranger matching and (ii) it is less pronounced in treatments with belief elicitation compared to control treatments where beliefs are not elicited. We also find that the restart has the effect of regenerating a sense of optimism among the subjects, which is reflected in increased contributions subsequently. This increase in contribution is driven mostly by those subjects who started the game with relatively more optimistic beliefs. Our results have implications for sustaining cooperation in social dilemma games.