Capita Return Research Articles

Increasing benefits in one-time public goods does not promote cooperation

The long tradition of research on cooperation includes a well-established finding that individuals respond to the degree of conflict between self- and collective interests (that is, the relative benefits from cooperation) in providing public goods. Existing empirical evidence builds upon settings where participants make multiple decisions or strategically consider alternative scenarios. Here, we consider a decision setting where participants face a one-time (single-decision) setting. One-time cooperative encounters often occur in volunteering or donating to immediate needs for crisis relief. For these distinct and highly relevant settings, we report a lack of responsiveness to increases in cooperation benefits, thereby highlighting limits to our understanding of the determinants of one-time cooperation encounters. Across two studies, n = 2,232 individuals participate in treatments where we vary across participants the relative benefit from contributing to a public good (that is, the marginal per capita return, the MPCR). We examine decisions from alternative participant pools (UK general population vs. students), implementations varying the physical distance between participants (online vs. in the laboratory), and more complex decision settings considering group-to-group interactions including not only providers but also donors to public goods. Throughout, neither average contribution levels, nor the distribution of contributions are significantly affected by the increases in cooperation benefits. The mechanism behind these results can be explained by the close correlation between expectations of other's cooperation and own cooperation, and the fact that these expectations do not increase with higher benefits from cooperation.

Frequency-dependent returns in nonlinear public goods games.

When individuals interact in groups, the evolution of cooperation is traditionally modelled using the framework of public goods games. These models often assume that the return of the public goods depends linearly on the fraction of contributors. In contrast, in real-life public goods interactions, the return can depend on the size of the investor pool as well. Here, we consider a model in which the multiplication factor (marginal per capita return) for the public goods depends linearly on how many contribute, which results in a nonlinear model of public goods. This simple model breaks the curse of dominant defection found in linear public goods interactions and gives rise to richer dynamical outcomes in evolutionary settings. We provide an in-depth analysis of the more varied decisions by the classical rational player in nonlinear public goods interactions as well as a mechanistic, microscopic derivation of the evolutionary outcomes for the stochastic dynamics in finite populations and in the deterministic limit of infinite populations. This kind of nonlinearity provides a natural way to model public goods with diminishing returns as well as economies of scale.

On the effectiveness of leading by example in public goods games

Despite the growing interest in leadership in the experimental literature, theoretical analyses of leadership have received relatively limited attention. This study investigates the effectiveness of leading by example in public goods games among reciprocal agents. The “leading-by-example” game (LBE) is a two-stage game with the same payoff structure as the classic voluntary contribution mechanism (VCM), in which a leader first makes a contribution decision, followed by the followers who make a contribution decision upon observing the leader’s move. If the marginal per capita return (MPCR) is sufficiently high, LBE is more effective than VCM at inducing contributions. However, if MPCR is low, VCM is more effective than LBE. An experimental test of the comparative statics is conducted.

Public goods and bads with vulnerable individuals: How information and social nudges change behaviour

AbstractIn a diverse society, heterogeneous returns to public goods (PG) and public bads (PB) are more often the rule rather than the exception, and often the returns from the public pool are such that individuals who are most affected no longer have incentives to free ride on others. We consider this set‐up through a laboratory experiment and investigate how heterogeneity of marginal per capita returns (MPCRs) affect economic cooperation in both PG and PB games. We also examine whether information on heterogeneity—no information, information and information with a plea to help those who are most affected by the public pool—changes cooperation. Our results show that information regarding the heterogeneity does not change individual behaviour in both PG and PB games. However, a social plea to help individuals with MPCRs of 1.20 increases average group efficiency. Average individual contributions under the social plea treatment are either maintained or increased. Those with MPCRs of 1.20 are more cooperative than their counterparts but not as completely as theoretically predicted. The exact same individual is also more cooperative under a PG game than under a PB game; a result that remains unchanged whether MPCRs are homogeneous or heterogeneous.

Cooperation is unaffected by the threat of severe adverse events in public goods games

In the context of a one-shot public goods game with a large group size and a low marginal per capita return, we study if and how cooperation is affected by the presence of environmental risk – defined as an exogenous stochastic process that generates a severe adverse event with a very small probability – and by the correlation of such risk among the group members. More specifically, we run an online experiment to investigate the effect of a risk that is independent across group members, a risk that is positively correlated among group members, and a risk that is negatively correlated among group members on cooperation. We find that neither the presence nor the correlation of risk significantly affects individual contributions.

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.

All-pay auctions versus lotteries as provisional fixed-prize fundraising mechanisms: Theory and evidence

We compare two fixed-prize mechanisms for funding public goods, an all-pay auction and a lottery, where public good provision can only occur if the participants’ contributions equal or exceed the fixed-prize value. We show that the provisional nature of the fixed-prize means that efficiency and endowment conditions must both be satisfied to assure positive public good provision. Our main finding is that provisional fixed-prize lotteries can outperform provisional fixed-prize all-pay auctions in terms of public good provision when endowments are large relative to prize values. We test these predictions in a laboratory experiment where we vary the number of participants, the marginal per capita return (mpcr) on the public good, and the mechanism for awarding the prize, either a lottery or an all-pay auction. Consistent with the theory, we find that the mpcr matters for contribution amounts under the lottery mechanism. However, inconsistent with the theory, bids are significantly higher than predicted and there is no significant difference in the level of public good provision under either provisional, fixed-prize mechanism. We consider several different modifications to our framework that might help to explain these departures from theoretical predictions.

How the incentive to contribute affects contributions in the one-shot public goods game

Enmeshed in various social structures, humans must often weigh their own interest against the interest of others—including the common interest of groups they belong to. The Public Goods Game (PGG), which succinctly pits individual interest against group interest, has been a staple of research into how people make such decisions. It has been studied in many variations, in the laboratory and (increasingly) online. One of the defining parameters of the PGG is the marginal per capita return of the group project (MPCR), which determines the incentive for contributing to the group project relative to the incentive of keeping points in the personal account. The effect of MPCR on contributions has been investigated before, but its effects have never been characterised with high resolution. Here, we present a systematic and high-resolution investigation of the effect of MPCR in groups of three. We do this in a large-scale online decision making experiment recruiting participants from Amazon Mechanical Turk. Our results provide a fine-grained account of the relationship between incentive to cooperate on the one hand and cooperation on the other, and can help to provide a basis for choosing MPCR magnitudes for future research endeavours using online PGG studies.

Cost-effective giving with multiple public goods

In this paper, we investigate how the choice environment affects contribution behavior in settings with multiple public goods. Specifically, we design a novel experiment that uses a standard voluntary contribution mechanism (VCM) game, except that subjects face multiple simultaneous VCMs, each with a different marginal per capita return (MPCR). We study two treatments—one with constrained contribution choices and one with a richer set of options—finding that the constrained choice environment yields higher payoffs. As a virtue of our design, we are able to decompose these payoff differences into two separate channels: differences in contribution levels versus differences in the cost-effectiveness of contributions. Although the first channel is typically the primary focus of public good analyses, we offer unique insights by showing that cost-effectiveness also plays an important role in shaping welfare outcomes in settings with multiple public goods. We find that cost-ineffective contributions significantly diminish payoffs in the richer choice environment—a result with important implications for modern charity and crowdfunding platforms, where donors are faced with an ever-growing number of charitable causes to consider.

Cooperation in Groups of Different Sizes: The Effects of Punishment and Reputation-Based Partner Choice.

Reputation and punishment are two distinct mechanisms that facilitate cooperation among strangers. However, empirical research on their effectiveness is mainly limited to relatively small groups and does not address how they enhance cooperation in relatively larger groups. We address this gap in the literature by testing hypotheses from competing perspectives about the extent to which reputation-based partner choice and punishment enhance cooperation in both small and large groups. Prior work recognizes that an increase in group size is accompanied by a change in the incentive structure, which determines whether the temptation (extra benefit for each person from non-cooperation over cooperation, regardless of others’ choices) or gain (extra benefit for each person from full cooperation over full non-cooperation) remains constant or varies with group size. Thus, we first test how group size affects cooperation when temptation or gain increases with group size (Study 1), and then move on to testing predictions on the effectiveness of reputation and punishment across different group sizes (Study 2). In Study 1 (N = 820), we randomly assigned participants to play an online one-shot public goods game in groups of 4, 20, or 40, while keeping the marginal group return or marginal per capita return fixed across groups, in which case the temptation or gain increased with group size. In Study 2 (N = 1,132), we further compared a public goods situation involving a punishment or reputation mechanism with an anonymous situation across group sizes, while the marginal group return was fixed across groups. Overall, we found that when temptation increased with group size, 20-person groups cooperated significantly less than 4-person groups in one-shot interactions, and that this effect was explained by lower expectation of others’ cooperation, less perceived collective efficacy, and greater perceived conflict. However, 40-person and 4-person groups did not vary in one-shot cooperation. Importantly, reputation-based partner choice and punishment invariably promoted one-shot cooperation in groups of different sizes. These findings suggest no simple effect of group size on cooperation and underscore the utility of reputation and punishment in fostering cooperation (at least in one-shot interactions) regardless of the size of groups.

Voluntary contributions in a system with uncertain returns: a case of systemic risk

This paper investigates systemic risk that emerges from the interplay between uncertain returns to individual actions, uncertainty on others’ behavior and all this filtered through individual attitudes toward risk. We design a finitely repeated linear public good experiment based on a voluntary contribution mechanism and analyze the effect of risky and uncertain returns on subjects’ contributions. Results from a baseline treatment without uncertainty are compared with two risky treatments characterized by different values for the marginal per capita return. In the treatments with risk, subjects are randomly assigned to one out of three feasible marginal per capita returns, independently of what their individual contribution was. Results show that a sufficient level of uncertainty leads to significantly lower individual contributions. Furthermore, in a system with lower contributions due to uncertainty, subjects’ risk aversion enhances the systemic risk, leading the system to collapse.

Cooperation in a risky world

AbstractWe offer a novel investigation of the effect of environmental risk on cooperation in the Voluntary Contribution Mechanism. Our baseline is the standard setting, in which the personal return from the public good is deterministic, homogeneous, and publicly known. Our experimental treatments alter this classic design by making the marginal per capita return from the public good probabilistic. In thehomogeneous risk(HomR) treatment, the random draw is made for the whole group, whereas in theheterogeneous risk(HetR) treatment, this happens independently for each group member. Our hypothesis is that different environmental risks may differently affect the ex post payoff inequalities, so that other‐regarding preferences (inequality aversion) may generate higher contributions in HomR than in HetR. Our main result is that the environmental risk does not affect the patterns of cooperation either in the one‐shot or in the finitely repeated version of the game. This suggests that the standard experimental methodology provides a robust and conservative measure of human cooperation.

Public Goods Provision with Rent-extracting Administrators

This article studies public goods provision when contributors repeatedly interact with rent‐extracting administrators. Our main finding is that the presence of an administrator reduces contributions but only because rent extraction lowers the marginal per capita return of investing in the public good. Analysing the interactions between the contributors and the administrator, we demonstrate that rent‐extraction and cooperation shocks trigger short‐run adjustments in agents’ behaviour. However, shocks do not have permanent effects. This explains the long‐run resilience of cooperation to rent extraction. We also show that cooperative attitudes and trust explain the heterogeneity in the short‐run volatility of public goods provision.

Can Non-Binding Promises Increase Cooperation in a Voluntary Contribution Mechanism Game? An Experiment

We consider a modified voluntary contributions mechanism (VCM) game where the marginal per capita return (mpcr) for a group of responders is endogenously determined by the proposer. We allow the proposer to implement a mpcr that is different to the mpcr initially announced, after observing responders’ contributions. Thus, the mpcr used to determine responders’ payoffs may differ from the mpcr that was public information when responders decided their contributions. Our findings indicate that contributions increase with the announced mpcr even when the announced mpcr is non-binding. This suggests that promising a high mpcr in VCM type interactions can be successful at increasing individuals’ contributions even if the eventual mpcr that determines payoff is substantially lower. Finally, we find that the marginal gains from the above strategy can be expected to decrease with experience.

Rewards and cooperation in social dilemma games

Rewards are identified as a mechanism to sustain cooperation in standard Public Good games, but have been found less effective in Common Pool Resource games. Both paradigms are important for environmental and resource economics as they capture the essence of real-world environmental and resource problems – the provision of pure public goods, and overextraction of common pool resources. This paper aims to understand why rewards are effective in one paradigm and not in the other. We hypothesize that this is because of an important difference between the two; the marginal per capita return is uncertain in the Common Pool Resource game because subjects can undo cooperative actions of others. This is just one of many differences between the two paradigms and hence we test our Hypothesis by introducing the option to reward in the Claim game, a game identical to the standard public good game except that it allows for both giving and taking. This feature causes the marginal per capita return to be uncertain. We find that while rewards are effective in sustaining cooperation in the Public Good game, they are much less effective in the Claim game. We identify the underlying mechanism causing this differential impact.

Does Uncertainty Deter Provision of Public Goods?

Nous étudions un jeu de bien public répété avec un horizon fini et connu (sous la forme du mécanisme de contribution volontaire) avec une incertitude complète sur le rendement marginal du bien public : ni le rendement marginal personnel, ni les rendements marginaux des autres joueurs ne sont connus au moment de la prise de décision sur la contribution individuelle au bien public. Nous montrons que les contributions sont similaires lorsque le rendement marginal du bien public est prédéterminé et parfaitement connu, et lorsqu’il est incertain. Dans les deux cas, les contributions ont tendance à décroître avec la répétition. En tenant compte des résultats expérimentaux précédents, nos résultats suggèrent que la coopération dans les jeux de biens publics est sensible à la source d’incertitude sur le rendement marginal du bien public.

Cooperation in a Risky World

We study the effect of environmental risk on cooperation in the Voluntary Contribution Mechanism. Our baseline is the standard setting in which the personal return from the public good is deterministic, homogeneous, and publicly known. Our experimental treatments alter this classic design by making the marginal per capita return from the public good probabilistic. In the homogeneous risk treatment, the random draw is made for the whole group, while in the heterogeneous risk treatment this happens independently for each group member. Our main result is that risk does not harm cooperation either in the one-shot or in the finitely repeated version of the game. This suggests that the standard experimental methodology provides a robust and conservative measure of human cooperation.

Experience and History

The development and use of long-lived public goods involves more than one demographic generation, leaving the classic literature on voluntary provisions partially unfit to explain complex phenomena such as welfare systems, climate policies and major infrastructure projects. This paper proposes a model that explains how equilibrium is reached in a context where heterogeneity is linked to seniority and strategic interaction is finitely repeated. Within this model the case of intergeneration public goods production is explained using a redistribution rule that benefits the younger players, as a compensation for their inexperience. Experimental evidence shows that subjects who belong to low or middling marginal per capita return types are negatively affected by heterogeneity, whereas groups benefit from the presence of experienced subjects. More importantly, results show that becoming disadvantaged (lowering the marginal per capita return of individuals in time) has negative effects on the provision of public goods, if compared to a situation where the disadvantage is constant in time (same low marginal per capita return in time).

Does Overconfidence Promote Cooperation? Experimental Evidence from a Threshold Public Goods Game

This paper studies the effects of two types of overconfidence — overestimation and overprecision — on investment in a public good in a two-person threshold public good game. Our experimental results show that the influence of overconfidence on investment in public goods crucially depends on the agents’ type of social preference. The marginal per capita return (MPCR) leads to a higher willingness to cooperate in conditional cooperators, but has little effect on the willingness of free-riders. The influence of overestimation on cooperation depends on the type of social preference that the agents have; overestimation leads to higher investment by conditional cooperators, but lower investment by free-riders. Finally, overprecision in general leads to higher investment by conditional cooperators, and tunes down the effect of changing MPCR on cooperation.

The tension between private benefits and degradation externalities from appropriation in the commons

This experimental study examines behavior in a linear public goods game with an appropriation frame where we vary the value of individual benefits and the group losses from appropriation. Parallel to the literature on public goods provision, individual appropriation decreases with the marginal damage to the group that occurs through appropriation and increases in the private benefit from appropriation. In addition, we examine a novel set of decision situations where individual benefits and group damages change proportionately, as to hold the marginal per capita return constant. Individual responses to these proportionate changes are heterogeneous but on average, appropriation levels do not change significantly. These results are robust to two experimental designs, a one-shot menu-design where subjects make multiple choices and a complementary set of sessions where participants make a single decision in a one-shot game.