1
Investigating the sustainability of cooperation with a
risk of contributions not reaching the public good
Master Thesis
Author: Gijs van Benthem Student number: 10583068
Supervisor: Ivan Soraperra
2 Statement of originality
This document is written by Gijs van Benthem, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
3 Abstract
In this thesis, a novel variant of the public good game experiment is conducted where a risk of contributions not reaching the public good is introduced. This paper examines how, in expected value-equivalent situations, participants contribute to the public good when they are faced with this risk. I find that participants contribute lower amounts, contribute relatively less compared to what they believe their group members will contribute and contribute zero more often when the risk is introduced.
4 Contents
1. Introduction 5
2. Literature Review 6
2.1 Background and similar studies 7
2.2 Decision-making under risk 8
2.3 Commitment and conditional cooperation 9
2.4 Altruism, warm-glow and reciprocity 10
3. Experimental design 10
3.1 Definitions and notation 11
3.2 Experimental procedures and details 12
4. Hypotheses 14 5. Results 15 5.1 Overview 15 5.2 Econometric tests 19 6. Discussion 22 7. Conclusion 23 8. References 25 9. Appendix 27
5 1. Introduction
Behavior in a public good setting has been analyzed and examined countless times in experimental and behavioral economics, mostly to determine influencing factors that cause certain contribution levels (Ledyard, 1997). Much is known about behavior in public good settings when there is complete information. Complete information, however, is an
unrealistic assumption in many social dilemmas observed in the real world (Boulu-Reshef & Brott, 2017). Returns from public goods are often intrinsically uncertain and the precise benefits of the public good to both the individual and the society are frequently hard to determine (Butera & List, 2017). Lack of information in a public good setting might occur because not everybody knows each other’s preferences or because that the value of a public good only becomes clear ex post (Boulu-Reshef & Brott, 2017). Another source of
uncertainty and incomplete information is the possibility that contributions do not reach the public good and, thus, resulting in a zero payoff. In reality, projects often fail or end up to be different than expected due to many different factors. The presence of this form of risk or uncertainty can be detrimental for the levels of contribution and cooperation (Gangadharan & Nemes, 2009).
Frequently used examples regarding the presence of uncertainty and risk in a public good setting are related to climate change. In these types of settings there is often the presence of environmental uncertainty, which could be introduced by having uncertainty regarding the threshold of a public good. For example, Dannenberg et al. (2014) investigated sustainability of cooperation in a public good setting where the threshold was uncertain. They found that when the threshold was uncertain, there was a lower level of cooperation and the public good was provided less frequently compared to when there was complete certainty about the threshold. Another example could be made on a whole different level which is more in line with the uncertainty in a public good setting modelled in this thesis, where an exogenous risk is present which causes the public good to be less trustworthy. It could be the case that contributions to the public good are wasted and end up not reaching the public good. For instance, consider a typical village in a developing country. When
deciding whether to contribute to a potential new road in the middle of the village, concerns are automatically raised about the non-transparency, possible corruption and inefficiency present in the local government. This causes a possibility of contributions made to the public
6 road to not actually reach it at all and therefore not benefiting the public. Behavior in a public good setting where this uncertainty is present seems interesting and insightful, since this form of uncertainty seems to occur often in the real world and could be a determining factor of behavior. Thus, behavior in a public good game where this risk is present is examined.
An important and insightful question is asked in this paper, which attempts to get closer to understanding the real world mechanics of behavior in a public good setting: can cooperation be sustained when there the possibility that contributions do not reach the public good?
Intuitively, a higher risk of contributions not reaching the public good should result in less contributions and lower levels of cooperation. This is mostly because of the general knowledge that people are, on average, risk averse over gains (Kahneman & Tversky, 1979). However, there are multiple factors that can still cause cooperation to be sustained on a high level, namely altruism, reciprocity and conditional cooperation. So even though the prediction of a drop in contribution is natural, an empirical analysis of behavior and
sustainability of cooperation in a public good setting where contributions may not reach the public good is an interesting research question that may provide valuable insights.
In my thesis, an experimental approach is taken to analyze the effect of the risk of contributions not making it to the public good on behavior. First, related literature is examined to investigate previous research on this topic and possible explanations of behavior in this type of setting. Second, an experiment is designed in a way that allows the effect of risk in contributions on behavior to be analyzed properly after which the results are discussed. Next, the hypotheses tested in this paper are listed and explained. Lastly, a final conclusion is made that discusses the implications of the results and suggestions for further research.
2. Literature review
The theoretical framework will be investigated in this section of the paper. First, similar papers are examined and discussed, after which a clear distinction is provided that separates this paper from existing literature. Moreover, a number of theories are invoked in an attempt to predict and explain behavior in the experiment conducted in this paper.
7 2.1. Background and similar studies
Decision-making in public good settings has been analyzed and studied countless times in the field of experimental economics, according to Butera and List (2017). In this thesis, however, there is a focus on analyzing several similar papers and examining possible explanations for behavior when different levels of risk of contributions not reaching the public good are introduced.
In economics, there is an interest in how people behave when a certain type of risk, uncertainty or ambiguity is introduced. However, these features seem to be absent in the vast majority of public good literature (Butera & List, 2017). To my knowledge, only a few deviations from complete certainty in a public good setting have been explored in the public good game literature. For instance, Fisher et al. (1995) conducted an experiment in which subjects did not receive complete information about the payoff functions of other subjects and the only information each subject received was their own payoff function. They found that individuals seem to behave only according to their own payoff function. Moreover, Levati et al. (2009) investigated the impact of incomplete information about the marginal benefit of the public good for all subjects on behavior. In their experiment, the total amount contributed to the public good is multiplied by a factor 𝑎𝑙𝑝ℎ𝑎. In the control treatment 𝑎𝑙𝑝ℎ𝑎 is fixed at 0.75, while in the second treatment 𝑎𝑙𝑝ℎ𝑎 can either be 0.4 or 1.1, each with probability 1
2. They conclude that imperfect information about the value of the public
good causes contribution to drop substantially. They explain this observation by relating risk attitudes to contribution behavior by saying that the more risk averse an individual is, the less she contributes.
Closer to the experiment presented in my thesis, Gangadharan and Nemes (2009) conducted an experiment in which the effect of risk and uncertainty in a public good setting were investigated by introducing a probability of not receiving the payoff from a the private or public account. Subjects had to decide between investing into a private or public account and subjects were given independent probabilities for the private and public account which determined whether the participant would receive the corresponding payoff from that specific account or otherwise ending up with zero payoff from that account. Probabilities of
8 both the public and private account were independent from each other and could be either 0.5 or 1.0. Their design allowed for analyzing behavior in a setting where there is uncertainty and risk about receiving the payoff from the public good, due to exogenous factors. One of their main findings is that when subjects face a possibility of not receiving the payoff from a certain account, contributions to that account decrease significantly.
The experimental design of Gangadharan and Nemes allowed for an analysis of behavior in a setting where there is a possibility of not receiving the payoff from the public or private account, due to exogenous factors. I look at uncertainty and risk from a different perspective. In my thesis, a deviation from existing literature is made by examining a public good game where the exogenous risk is on whether contributions reach the public good, instead on whether agents receive the payoff from the public good. In reality, there could always a possibility of contributions being wasted and not reaching the public good. Therefore, my thesis is aimed to get one step closer to understanding behavior in a public good setting where this risk is present.
2.2. Decision-making under risk
The experiment conducted in this paper keeps the expected value of the public good constant over all treatments, assuming risk neutrality and constant behavior over the whole experiment. This means that Expected Value Theory predicts the same results in every treatment. In theory, behavior should not change if a risk of contributions not reaching the public good is introduced, keeping the expected value constant. However, even though Expected Value Theory is considered one of the best generalized expected utility theories in Economics, it still often fails to accurately predict behavior (Harless & Camerer, 1994). One reason why Expected Value Theory might consistently not predict well is the fact that many individuals are risk averse, even with low stakes (Holt & Laury, 2002). According to Holt and Laury (2002), the presence of risk aversion causes the assumption of risk neutrality, which is one of the assumptions of Expected Value Theory, to be problematic for predicting behavior.
Even though the effect of risk aversion is mostly analyzed in individual descion-making settings, a few papers investigated and tested some of its elements and features in strategic settings (Iturbe-Ormaetxe et al., 2011). For instance, Gangadharan and Nemes (2009) analyze the effects of risk aversion on behavior in a public good setting by testing the hypothesis whether risk attitudes and preferences influence the amount invested in the
9 private account and the public account when an exogenous risk is present. Their results show that in payoff-equivalent situations, their participants contributed less to the public good when there was uncertainty or risk associated with the public good. They conclude by stating that public good setups where risk, uncertainty and variability is high, contributions and cooperation diminishes.
Based on this evidence and on results in the individual decision-making literature, I expect that with the setting presented in this paper, the presence of a risk of contributions not reaching the public good will cause individuals to contribute less and therefore diminish cooperation levels.
2.3. Commitment and conditional cooperation
Individuals often choose their actions based on what they prefer everyone else would choose (Laffont, 1975). This notion is called commitment theory and is consistent with many observations in voluntary cooperation and contribution dilemma’s like public goods (Croson, 1998). Laffont (1975) found that when an individual believes that others will act similarly to their own behavior, voluntary contributions increase and social welfare generally increases.
Many theories regarding commitment of actions in this type of setting argue that individuals often have an unconditional commitment strategy, meaning that their action does not depend on what others have done in the past (Sugden, 1982). One of these theories describes the principle of ‘rational commitment’, which implies that individuals contribute the amount that others are preferred to contribute (Harsanyi, 1980). However, this strategy is only applied if an individual chooses a strategy in the beginning of the game with a firm commitment to follow this strategy for the whole duration of the game, even when it is tempting to deviate from this strategy. Assuming that individuals apply an unconditional commitment strategy seems unrealistic since it is likely that individuals will base their own actions on what other have done in the past. Therefore a less strict and more flexible strategy such as conditional cooperation could be seen as another way to predict and explain behavior in this type of setting. Cettolin and Riedl (2011) define conditional cooperation as being ready to contribute if one believes that others will contribute.
Fishbacher, Gachter and Fehr (2001) used a simple public good experiment to show that a substantial portion of people use a contributing strategy that can be classified as conditional cooperation. Their data showed that around 50 percent of their subjects were
10 conditional cooperators and that these individuals would contribute based on the average contribution behavior of the rest of the group. There are also other observed variations of this specific behavior, which is still classified as conditional cooperation. Cartwright and Lovett (2014) state that the insight and knowledge on conditional cooperation can help to understand the dynamics of behavior in public good settings.
Conditional cooperation predicts that people change their strategy once they observe changes in the actions of others. Due to my prediction that people contribute less when the risk is introduced, I predict that people commit to a lower contribution level and will
decrease contributions over time, using conditional cooperation. In my thesis, commitment behavior is analyzed and it is examined how often conditional cooperation is applied in both treatments.
2.4. Altruism, warm-glow and reciprocity
In general, individuals care directly about the utility of others. This is shown by the frequent observation that an individual’s utility is not only dependent on his own
consumption or outcome, but also on the consumptions and utility of others (Becker, 1974). Many models using altruism to predict and explain certain behavior have been constructed and have been influential in analyzing economic behavior in many settings (Croson, 1998). However, many results have shown the lack of predictive power of altruism models and therefore Anderoni (1990) attempted to make a more general model which incorporates not only the other’s utility but also the utility of giving into one’s utility function. This utility gained from giving is often referred to as ‘warm-glow effect’.
A similar driver of behavior is the urge to reciprocate or match the contributions of others (Croson, 1998). Reciprocating is a way of gaining utility from giving or contributing, simply by attempting to fit in the norm of the group, according to Sugden (1984).
All these behavioral factors imply that individuals care about the outcome for others and that individuals assign value to giving, especially if they observe others doing it. These behavioral factors thus predict that individuals keep contributing nonzero amounts, as long as some level of cooperation is present.
11 3. Experimental design
In this part of the paper, an overview is given about the specifics and the logistics of the experiment. First, a description and definition of all the relevant variables is given and the notation is explained. This will better clarify the model and the rational of the design used in this experiment. Next, a description of the general experimental procedure is given, after which details regarding the treatments are provided.
3.1. Definitions and notations
In a standard public good game only endogenous strategic uncertainty is present, meaning that individuals only face uncertainty about the contribution behavior of others. In this experiment an exogenous risk is introduced by adding a probability that the
contributions do not reach the public good. This public good game experiment consists of two treatments: one baseline treatment, which is a standard public good game with no exogenous risk and a risk treatment where an exogenous risk of contributions not reaching the public good is introduced.
In this experiment all participant receive an endowment (𝜔) consisting of tokens and have to decide how to allocate their endowment by choosing between a private account (𝑥) or a group account (𝑔). Participants are forced to allocate all the tokens and this results in the following budget constraint:
𝜔𝑖 = 𝑥𝑖+ 𝑔𝑖
A token allocated to the private account gives a payoff of 1 to the participant that allocated it with certainty, while a token that is allocated and that reaches the public good gives a payoff of 0<𝑎𝑙𝑝ℎ𝑎<1 to all participants. Tokens that are allocated to the public good and do not reach it are lost and give a payoff of 0.
If a participant decides to contribute, thus allocating one or more tokens to the public account, the contribution reaches the public good with a probability 𝑃𝑔. This probability is completely independent for each participant. Therefore, for each participant, the expected value of the public good depends on the participant’s own investment 𝑔𝑖, on the probability
that this contribution reaches the public account (𝑃𝑔) and on the expected amount of tokens
provided in the public account by others (𝐸(𝑔𝑗)), given their contributions. These parameters result in the following expected payoff:
12 𝐸(𝑔𝑖) = 𝑃𝑔[𝜔𝑖− 𝑔𝑖+∝∙ 𝑔𝑖+ ∝ 𝐸(𝑔𝑗)] + (1 − 𝑃𝑔)[𝜔𝑖 − 𝑔𝑖+ ∝ 𝐸(𝑔𝑗)]
The optimal contribution behavior is computed by taking the derivative of the expected valuation to the amount contributed to the public account and setting it equal to zero:
𝜕𝐸(𝑔𝑖)
𝜕𝑔𝑖 = 𝑃𝑔[1−∝] + (1 − 𝑃𝑔)[−1] = 𝑃𝑔 ∝ −1
Given that in the baseline treatment the probability that a contribution reaches the public good is 100 percent (𝑃𝑔 = 1) and 𝑎𝑙𝑝ℎ𝑎 is between 0 and 1, the optimal contribution
behavior where no risk is present is 𝑔𝑖 = 0.
In order to keep the marginal incentive to contribute constant across both
treatments, we set the MPCR of the treatment with exogenous risk equal to the baseline. So, if 𝑃𝑔 is the probability that the contribution reaches the public good and 𝑎𝑙𝑝ℎ𝑎’ is the MPCR
in the baseline, the MPCR in the treatment with exogenous 𝑎𝑙𝑝ℎ𝑎 is:
∝ =∝ ′ 𝑃𝑔
As before, the optimal contribution of a selfish risk neutral is 𝑔𝑖 = 0. Given that the
expected marginal incentive is kept constant across both treatments, allows for a more insightful and powerful comparison of behavior between the two treatments.
3.2. Experimental procedures and details
A lab experiment is conducted in order to test the hypotheses regarding the research question of this paper. Participants for this experiment are friends and relatives and are incentivized by the knowledge of possibly being monetarily rewarded according to their performance.
The first treatment of this experiment is the baseline treatment, in which every participant plays a standard public good game without the presence of exogenous risks and uncertainties. In this treatment, each participant starts receives an endowment of 100
13 tokens (worth 10 real euros) after which they are asked to decide how to allocate this
endowment between a private and public account. Moreover, every participant is informed about the value of the public good. Each unit contributed to the public account by any participant is multiplied by a factor 0.4 (𝑎𝑙𝑝ℎ𝑎 = 0.4), thus each token invested in the public good yields a return of 0.4 for each participant.
In the risk treatment every participant is informed about the introduction of an exogenous risk that can cause contributions not to reach the public good. Furthermore, just like in the baseline treatment, each participant receives an endowment of 100 which has to be allocated between a private and public account. Again, every participant is informed that each token invested in the public good will be multiplied by a factor, though now by a factor of 0.8 (𝑎𝑙𝑝ℎ𝑎 = 0.8), thus each token reaching the public good yields a return of 0.8 for each participant. Moreover, there is an exogenous risk present of 0.5 (𝑃𝑔 = 0.5), meaning that every participant has a 50 percent chance of his or her contribution to the public account not making it to the public good. In order for the marginal per capita return of the public good to be constant over the whole experiment, 𝑎𝑙𝑝ℎ𝑎 is set at 0.8 instead of 0.4. The assumptions made in order for these parameters for 𝑎𝑙𝑝ℎ𝑎 to keep the expected valuation of the public good constant over both treatments are risk neutrality and constant
contribution behavior over both treatments.
In both the baseline and the risk treatment, groups of four participants play ten consecutive rounds per treatments in fixed groups. In each round, participants, who are identified with a randomly generated ID number, are given their own personal endowment of 100 tokens after which they are asked to choose how to allocate their own tokens between a private and public account. In the end of every round, the total amount of contributions (total amount of tokens allocated to the public account) is calculated.
Additionally, it is randomly generated which contributions reach the public good in the risk treatment. Lastly, the total value of the public good and the value per participant of the public good are calculated and announced in the corresponding round. At the end of every round, participants are informed about the sum of the contributions which reached the public good and about their payoff. Thus, in the baseline participants are aware of the total amount contributed by the group. However, in the risk treatment there is uncertainty about the amount the group members contributed to the public good.
14 As stated before, participants were incentivized with a probability on a monetary reward. The instructions stated that participants can earn money in the experiment and that three participants out of the whole subject pool will be randomly selected and paid after conducting the experiment. These selected participants were paid for their outcome in one randomly selected round. Furthermore, in the instructions the game and procedure are explained and information about all possible payoffs and risk levels are clearly provided. In this experiment, there is no exogenous uncertainty about any factor, meaning that factors such as the risk of contributions not reaching the public good are provided in the instructions to all participants and are thus common knowledge.
4. Hypotheses
With this experimental design and the use of these experimental procedures, the following hypotheses are tested in order to gain more insight on behavior in a public good setting when a risk of contributions not reaching the public good is introduced. Each hypothesis is tested by comparing data from the baseline treatment to the risk treatment.
As examined in the literature review, previous studies show that when risk or uncertainty is introduced in a public good setting, cooperation and contributions generally diminish. Hypothesis 1, which is the main hypothesis of this paper, is aimed to test whether individuals invest less in the public good when an exogenous risk of contributions not reaching the public good is introduced.
Hypothesis 1: In an expected payoff-equivalent situation, participants contribute
significantly less to the public good when an exogenous risk of contributions not reaching the public good is introduced.
Furthermore, with hypothesis 2 it is tested whether there is a faster convergence to the Nash equilibrium (which is a contribution of zero to the public account) in the risk treatment. Commitment and conditional cooperation theory predict that people behave as they want others to behave and base their action by observing what others have done in the past. It is expected that individuals cooperate and contribute less in the risk treatment (hypothesis 1), thus individuals would likely commit to a lower contribution level and would
15 most likely decrease contributions over time when observing that cooperation decreases significantly faster in the risk treatment, using conditional cooperation.
Hypothesis 2: There is a significantly faster convergence to the Nash equilibrium if a risk of contributions not reaching the public good is introduced.
Lastly, the presence of altruism, warm-glow and reciprocity is tested in this paper by testing hypothesis 3. It is difficult to distinguish these factors, so a simplification is made by solely testing if there is a change in the proportion nonzero amounts contributed to the public good between the two treatments.
Hypothesis 3: The proportion of nonzero contributions to the public account is
significantly lower if the risk of contributions not reaching the public good is introduced.
5. Results
In this section, first an overview of the data from the experimental sessions is presented. Next, a more sophisticated approach is taken to formally test the hypotheses.
5.1. Overview
To examine Hypothesis 1, a comparison is made between the average contribution between both treatments. Figure 1 presents the average individual contribution to the public account for both treatments.
16
Figure 1: Average contribution to the public account
As displayed in Figure 1, the average contribution to the public account in the
baseline treatment is approximately 45 tokens. Moreover, in the risk treatment, the average contribution to the public account is approximately 31 tokens. Thus, the average
contribution dropped by 31 percent when the risk is included. These observations suggest that subjects invest more in a public good when certainty is present compared to when there is a risk that contributions do not reach the public good, even though the expected valuation remains constant between both treatments.
In Hypothesis 2, it is predicted that there is a faster convergence to the Nash
equilibrium in the risk treatment. To test this, Figure 2 shows the average contribution to the public good over time. Each treatment consisted of 10 rounds.
0 5 10 15 20 25 30 35 40 45 50
Baseline Risk treatment
Av era ge con trib u tio n
Average contributions
17
Figure 2: Average contribution levels over time (10 periods)
Initially, contribution levels are substantially higher in the baseline treatment. However, Figure 2 shows that contribution levels in both treatments converge to a similar level over time. This timeline shows that average contribution levels in the baseline
treatment have a slightly negative trend over time, while there is a slightly positive trend in the risk treatment.
Related to Hypothesis 2, the relation between beliefs and contribution behavior is examined. Tables 1 and 2 show the correlation between the amount contributed and the corresponding beliefs. More specifically, the correlation between the amount a participant contributed to the public account and what this individual believed that the others would invest in the public account in the corresponding round. To investigate this the relation between contribution and beliefs, the following regression is used:
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑖 = ∝ + 𝛽 ∙ 𝐵𝑒𝑙𝑖𝑒𝑓𝑖
The dependent variable in this model, 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑖, denotes the amount
contributed to the public account by an individual. Moreover, ∝ represents the intercept and 𝛽 denotes the effect of one’s beliefs about the average contribution of his/her group members in the corresponding round (𝐵𝑒𝑙𝑖𝑒𝑓𝑖) on his/her contribution behavior.
0 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 10 Av era ge con trib u tio n Round
Average contribution over time
18 This regression was conducted for each treatment. Both outputs are given in Table 1 below: Baseline Risk Belief 0.921* (0.077) 0.844* (0.066) α 1.62 (4.034) 3.113 (2.684) Notes:
Numbers in parentheses are standard errors *: significant at the 5% level
Table 1: Correlation between beliefs and contributions
Both outputs show that there is a strong correlation between beliefs and
contribution behavior in both treatments. However, this result has to be interpreted with caution, because there is no control for repeated choices and both reverse causality and endogeneity issues, which are all likely present. These tables are simply intended to describe and display the strong correlation between beliefs and contributions in both treatments and no conclusions can be drawn in terms of causality.
Lastly, Hypothesis 3 predicts that more contributions of zero are made in the risk treatment. With Figure 3, it is shown how often a zero and nonzero contribution to the public good occurred in each treatment, as a percentage of the total amount of
19
Figure 3: Percentage of zero and nonzero contributions
In the baseline treatment, approximately 78% of all observations consisted of a nonzero contribution and thus 22% being zero contributions. In the risk treatment,
approximately 72% was a nonzero contribution, while the remaining 28% consisted of only zero contributions.
5.2. Econometric Tests
In order to determine whether the collected data is in line with the three hypotheses formulated above, regression analysis and non-parametric tests are conducted.
First, since every participant participated in both treatments of this experiment, a Wilcoxon matched-pair signed-rank test is performed to test the effectiveness of adding an exogenous risk of contributions not reaching the public good. This experiment was done on six groups, which all participated in both treatments. However, the order of the treatment was randomized (three groups started with the baseline treatment and three groups started with the risk treatment). This Wilcoxon test is performed on the total contributions of the group in each treatment.
In this experiment, each group contributed less in the risk treatment compared to the baseline. The Wilcoxon signed-rank test on the contributions on group level results in a rejection of Hypothesis 1, suggesting that contributions are significantly lower in the risk treatment (p-value=0.0277). 0 10 20 30 40 50 60 70 80 90 100 Baseline Risk Perc en ta ge o f all con trib u tio n s
Nonzero contributions
20 Next, results from multiple fixed effects least squares regressions are presented. In each of these regressions, the dependent variable is the individual contribution made to the public account. First, only a treatment dummy is included in the regression in order to measure the treatment effect in this experiment, while controlling for fixed effects on individual and group level. Aside from the treatment dummy, the other regressors used in these regressions are: the beliefs of individuals about the contributing behavior of others and the round number. The results of the three regressions are summarized in Table 2.
Model 1 Model 2 Model 3
Treatment -13.36* (2.411) -20.009* (10.062) 2.307 (9.872) Round -0.682 (0.594) -0.611 (0.543) RoundTreatment 0.869 (0.840) 0.023 (0.775) Beliefs 0.653 (0.080) BeliefsTreatment -0.035 (0.098) Notes:
Numbers in parentheses are standard errors *: significant at the 5% level
Table 2: Fixed effects regressions
Results relating to the first hypothesis are presented in the Table 1 as model 1. In this model, the Treatment dummy has a significant negative effect on the contribution level of participants, suggesting that participants contribute significantly less when they face a public good with risk when compared to a public good without risk, assuming that the expected valuation is the same between the two treatments.
The Wilcoxon singed-rank test and the regression model 1, displayed in Table 2, give better insight on the effect of introducing a risk of contributions not reaching the public
21 good on contribution behavior. The significance of the Wilcoxon signed-rank test and the significant negative estimate in model 1 suggest that participants contribute less to the public good when the risk is introduced. Possible causes of the decrease in contribution could be possible risk aversion of participants in a public good setting or possibly that conditional cooperators expect their group members to contribute less and hence will contribute less themselves.
Related to Hypothesis 2, model 2 (Table 2) does not support the hypothesis that there is a faster convergence to the Nash equilibrium in the risk treatment. The positive, but insignificant, coefficient of the interaction term between round and treatment indicates that the slope is steeper in the baseline treatment and thus suggesting that there is a faster convergence to the Nash equilibrium in the baseline treatment.
Furthermore, as a part of Hypothesis 2, with model 3 it is tested whether beliefs have a different effect between treatments. The estimated coefficient for the interaction term between beliefs and treatment is negative, which indicates that the participants’
contributions react less to beliefs in the risk treatment. This finding is in line with the hypothesis that participants are less (conditionally) cooperative when risk is introduced. However, the estimate of this interaction term is not significant and thus no strong conclusions can be made from these results.
The final econometric test is to examine whether participants were significantly less altruistic and showed less reciprocity and warm-glow in the risk treatment (Hypothesis 3). As mentioned above, this is done by testing whether non-zero contributions are significantly common in the risk treatment. A Wilcoxon singed-rank test is conducted in order to test this hypothesis, where the amount of nonzero contributions of each group was compared between both treatments.
In the risk treatment, slightly more contributions of zero were made compared to the baseline. Though, the results from the Wilcoxon singed-rank test only support the
hypothesis that participants contribute significantly less nonzero amounts in the risk
treatment with low statistical value (p-value=0.462). Looking at the raw data, it suggests that participants contribute zero more often in the risk treatment, implying that there could be less altruism, warm-glow and reciprocity present in a risky public good setting. However, due to the insignificance of the Wilcoxon signed-rank test, no strong conclusions can be
22 6. Discussion
An experiment was conducted in this paper, where 24 participants played a public good game in groups of four. This paper adds to the existing literature on behavior in public good games by including an exogenous risk of contributions not reaching the public good. After examining existing literature on behavior in a public good setting, a few main
hypotheses were formulated. Behavior in the conducted experiment was mostly in line with the predictions: participants contributed less in the risk treatment, participants contributed slightly less when compared to their beliefs about the behavior of others in the risk
treatment and there were slightly more contributions of zero in the risk treatment. However, it should be noted that most estimates were not significant, constraining the power of these findings.
The important question in this section is whether these observations can be
generalized and conclusive. First, in this experiment all participants were friends or relatives, causing the quality of the data to be sub-optimal. Participants always knew their group members and this could have had possible effects on behavior, which are not controlled for. Second, with 24 participants, the number of subjects and observations is relatively small. Many insignificant estimates in the econometrical analysis part of the paper may likely be due to the lack of observations. A similar experiment with more participants and
observations may have provided stronger results and more conclusive evidence. Also, each subject participated in both treatments and groups remained the same during both
treatments. Having a within-subject design in a public good game experiment could have many effects on behavior that are hard to control for. Possible problems caused by the within-subject design could be because the behavior of participants in their second treatment was influenced by namely learning, reputation, the preference to behave
consistently throughout the whole experiment and receiving possible cues that reveal what the experimenter is investigating. A better approach would be to have a design where each participant only participates in one treatment.
Aside from the flaws and shortcomings in the experimental design, the amount of explanatory factors that were included in the literature review, design and the analysis might have been too much. Since not one behavioral factor is isolated in this design, it is not
exactly clear what behavioral factor was the cause of certain observations, making the results less clear and conclusive.
23 7. Conclusion
In this paper, a laboratory experiment is conducted where an exogenous risk of contributions not reaching the public good is added to a standard public good game. The expected value of the public good remained constant during the whole experiment, allowing for a strong comparison between the two treatments.
All findings are related to the hypotheses, formulated above. First, the average contribution is significantly lower in the risk treatment. Risk aversion of participants in a public good setting or the application of conditional cooperation when expecting that group members contribute less when the risk is present could be possible explanations for the drop of contributions in the risk treatment. Second, in both treatments, no convergence to the Nash equilibrium was found. Cooperation and average contribution remained relatively constant over time in the two treatments. Furthermore, it is found that participants
contribute relatively less compared to what they believe their group members will contribute in the risk treatment. Lastly, it is observed that there is a larger, though not significant, percentage of contributions of zero made to the public good in the risk treatment when compared to the baseline. Possibly suggesting that there could be less altruism, warm-glow and reciprocity present in a public good setting where a risk of contributions not reaching the public good is introduced.
The results from this experiment could be used to obtain more insight on behavior mechanics in a public good setting where exogenous risk is introduced. In many real life public good settings a form of risk is present, possibly causing contribution levels to be substantially lower. Policy makers involved in public good settings could use this information in order to achieve less risk and uncertainty and possibly higher contribution levels. For instance, making the public good setting as transparent as possible by making the
contributions common knowledge. Taking away this kind of uncertainty from the public good setting may increase the level of contribution and cooperation.
A recommendation for further research is to isolate the factors that determine behavior in a public good setting with risk. In this paper, a relatively wide spectrum of behavioral factors is included and analyzed. Future research could focus on isolating certain relevant behavioral factors. A possible suggestion for further research is to focus on
sustainability of cooperation over time in a risky public good game by adding more rounds and investigate whether contribution and cooperation levels are affected by the risk.
24 Another suggestion for further research is to separate the effect of altruism, warm-glow and reciprocity and explore the relative impact of these factors in a public good setting when the risk is introduced. For instance, in order to measure possible altruism effects, endowment differences could be introduced. Moreover, a possible way to investigate the effect of warm-glow in this setting, is to conduct a charity experiment where the risk of contributions not reaching the charity is introduced.
25 8. References
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26 Harsanyi, J., 1980, Rule Utilitarianism, Rights, Obligations and the Theory of Rational
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Iturbe-Ormaetxe, I., Pointi, G., Tomás, J., Ubeda, L., 2011, Framing Effects in Public Goods: Prospect Theory and Experimental Evidence. Games and Economic Behavior, 72(2), 439-447.
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27 9. Appendix
Materials included in this section are the instructions and the decision sheet for this experiment. Regarding the instructions, Part 1 represents the instructions for the baseline and Part 2 for the risk treatment. The decision sheets remained the same during the whole experiment, except for the round number.
Instructions
Welcome to this experiment!
Thank you for participating in this experiment. Before we start, I would want to ask you to refrain from any form of communication with other participants for the duration of the whole experiment. I would also like to mention that no cellphone usage is allowed during this experiment, so please turn off your cellphone and put it in your bag. Please read the instructions carefully, as it contains
everything you need to know to participate. You have all received your individual ‘Player ID’, which will remain the same for the whole duration of the experiment and is used to track your decision-making. The whole experiment consists of 2 parts. Each part has 10 rounds. Lastly, after all the data of all the groups are collected, three randomly selected participants are picked for payment based on their outcome in one randomly selected round and will be contacted via email.
Part 1
This part consists of 10 rounds. You are matched with three other participants for the whole duration of this part of the experiment. Each of you receives a total amount of 100 tokens in the beginning of each round, after which you are individually asked to decide on how to invest the tokens that you are given. Note: every 10 tokens are worth 1 real euro. There is a private and public account. Each token invested in the private account yields a one token return. Moreover, each token invested in the public account yields a 0.4 token return for each group member, including the investor.
Example 1: Every participant invests 20 tokens in the private account and 80 tokens in the public
account. The payoff for each participant: 20 + 0.4 × (80 + 80 + 80 + 80) = 20 + 128 = 148 tokens.
Example 2: Participant 1 invests 10 tokens in the private account and 90 tokens in the public account.
Participants 2, 3 and 4 invest 50 tokens in the private account and 50 tokens in the public account. The payoff for participant 1: 10 + 0.4 × (90 + 50 + 50 + 50) = 10 + 96 = 106 tokens. The payoff for participants 2, 3 and 4: 50 + 0.4 × (90 + 50 + 50 + 50) = 50 + 96 = 146 tokens. You will all shortly receive your own decision sheet on which you have to fill in your own:
Player ID
Investment in the private account Investment in the public account
Believes about average contribution of the other group members in the corresponding round After every participant has completely filled in the decision sheet, all sheets are collected. Next, information is provided about how much was invested in the public account and the total value of the public good in the corresponding round. The provision of this information will be the end of the round.
28 If you have any questions, please raise your hand and your questions will be addressed. After it is made sure that the instructions are clear, you will receive the first decision sheet.
Part 2
This part consists of 10 rounds. You are matched with three other participants for the whole duration of this part of the experiment. Each of you receives a total amount of 100 tokens in the beginning of each round, after which you are individually asked to decide on how to invest the tokens that you are given. Note: every 10 tokens are worth 1 real euro. There is a private and public account. Each token invested in the private account yields a one token return. Moreover, each token invested in the public account yields a 0.8 token return for each group member, including the investor. Lastly, there is now a possibility of investments not reaching the public account. More specifically, each participant that invests in the public account has a 50% risk of his/her investment not reaching the public account.
Example: Participants 1 and 2 both invest 30 in the private account and 70 in the public account.
Participants 3 and 4 invest 60 in the private account and 40 in the public account. The contributions of participant 2 and 3 do not reach the public good. The payoff for participants 1 and 2: 30 + 0.8 × (70 + 40) = 30 + 88 = 118 tokens. The payoff for participants 3 and 4: 60 + 0.8 × (70 + 40) = 60 + 88 = 148 tokens.
You will all shortly receive your own decision sheet on which you have to fill in your own: Player ID
Investment in the private account Investment in the public account
Believes about average contribution of the other group members in the corresponding round After every participant has completely filled in the decision sheet, all sheets are collected, after which it is randomly generated which who’s contributions reach the public account and who’s don’t. This is done for rolling a die for every participant: an odd number means that his or her contribution does not reach the public good. Next, information is provided about how much reached the public account and the total value of the public good in the corresponding round. The provision of this information will be the end of the round.
If you have any questions, please raise your hand and your questions will be addressed. After it is made sure that the instructions are clear, you will receive the first decision sheet.
29 Decision sheet
