Threshold and Group Size Uncertainty in Common-pool Resources: An Experimental Study

Abstract

Threshold common-pool resources (TCPRs), such as fisheries or groundwater reserves, face irreversible damage if harvesting exceeds a sustainability threshold. Uncertainty about the threshold for sustainable use or the number of resource users can exacerbate the overharvesting problem. Policy makers may therefore seek to reduce threshold or group size uncertainty in TCPRs. Overall, we find that reducing threshold and group size uncertainty (moving from high to low uncertainty) increases expected earnings from the resource. However, complete elimination of group size uncertainty reduces expected earnings. Furthermore, the impact of group size uncertainty on earnings varies by the level of threshold uncertainty. Moving from high to low group size uncertainty increases earnings at low levels of threshold uncertainty but not at high levels of threshold uncertainty. Taken together, we find that reducing threshold uncertainty is beneficial while tackling group size uncertainty requires a more nuanced approach, highlighting the importance of a joint analysis.

Keywords

uncertainty common-pool resources social dilemma group size

All over the world, a wide variety of resources such as fisheries (Worm 2016), groundwater reserves (Famiglietti 2014), and forests (Nobre et al. 2016) are under severe pressure and are at risk of irreversible damage (ten Broeke et al. 2018). Preventing depletion of these resources is of critical importance to policy makers (Terama et al. 2016).¹ Sustainable use not only helps ensure economic prosperity (Hughes and Johnston 2005) but can also help avoid conflict and war (Giordano, Giordano, and Wolf 2005). Relying exclusively on state regulations or market-based solutions has proven to be inadequate for effective management of common-pool resources (Ostrom 2008). Policy makers may thus seek to facilitate community self-governance to encourage cooperative behavior among resource users (Ostrom 1994; Colin-Castillo and Woodward 2015). However, environmental uncertainty poses a major challenge to such cooperative efforts (Barrett and Dannenberg 2012). Environmental uncertainty refers to the situation when some aspect of the resource such as its size, the number of users, the regeneration rate, or the payoffs from the harvests is not known with certainty (Walker and Gardner 1992).² Adverse consequences of environmental uncertainty include overharvesting in fisheries (Ludwig, Hilborn, and Walters 1993) and excessive withdrawals from groundwater reserves (Richey et al. 2015).

Given the prevalence of environmental uncertainty, understanding individual decision-making under uncertainty is essential (Fulton et al. 2011). This study contributes to this discussion by examining individual behavior under uncertainty in an important class of common-pool resources known as threshold common-pool resources (TCPRs).³ A TCPR is a resource that can be used safely up to a certain level, the threshold, but is damaged beyond it (Suleiman and Rapaport 1988).⁴

Two prominent forms of environmental uncertainty in TCPRs are threshold uncertainty (Aflaki 2013; Lenton 2013) and group size uncertainty (Takigawa and Messick 1994). Both threshold and group size uncertainty influence individual decision-making. In lab studies, high threshold uncertainty leads to excessive use and more frequent destruction of the resource (Botelho et al. 2014). Group size uncertainty, however, reduces withdrawals and the resource is less likely to be destroyed (Au and Ngai 2003). In the field, TCPRs are marked by multiple forms of environmental uncertainty simultaneously (Wilson 2002; Hopfensitz, Mantilla, and Miquel-Florensa 2019). It is, therefore, important to assess the joint impact of uncertainties. Our key contribution is precisely that we study the joint impact of threshold and group size uncertainty.

This study employs a laboratory experiment. There is a well-established tradition of laboratory experiments informing environmental policy-making (List and Price 2013; Noussair and van Soest 2014) and common-pool resource management policies (Ostrom 2006; Cárdenas 2016). Experimental methodology is ideal to address this issue because we can exogenously vary the type of uncertainty (threshold vs. group size) and its magnitude (low vs. high uncertainty), allowing causal inference. Such control is not possible in the field (Maas et al. 2017).

This experiment uses a within-subjects design where each subject participates in all the experimental conditions. There are three TCPR games in this experiment. The three games differ in what element(s) of the TCPR game is (are) uncertain—the threshold, the group size, or both the threshold and group size. Within each game, we vary the magnitude of uncertainty about the threshold and group size.

Overall, we find that an increase in threshold uncertainty increases the chance of the resource being destroyed and reduces expected earnings. In a TCPR with threshold uncertainty, the presence of group size uncertainty reduces the likelihood of resource destruction and increases expected earnings. The main policy implications are that reducing threshold uncertainty is beneficial but eliminating group size uncertainty may be inexpedient. Additionally, we find that threshold and group size uncertainty interact. For instance, group size uncertainty reduces withdrawals from the resource but only when the threshold uncertainty is low. At high levels of threshold uncertainty, the presence of group size uncertainty does not have a significant effect. This highlights the necessity of a joint analysis when there are multiple uncertainties.

The next section reviews the related literature. The third section presents the experimental design. The fourth section discusses the results, and the final section is the closing discussion.

Related Literature

This article bridges two sets of studies, the work on threshold uncertainty and on group size uncertainty in TCPRs. Prior work has examined threshold and group size uncertainty in isolation. When there is threshold uncertainty, there is no group size uncertainty and vice versa. Since multiple uncertainties exist simultaneously in TCPRs, we need to investigate whether and how the joint presence of multiple uncertainties influences individual behavior. Hence, in the experiment, both the threshold and group size are uncertain, making a joint analysis possible. We now present a brief overview of the related literature.

TCPRs with Threshold Uncertainty

The literature on TCPRs with threshold uncertainty is fairly large and is reviewed in Mantilla (2018). Most of the uncertain TCPRs have been operationalized with a uniformly distributed threshold and crossing the threshold leads to full destruction of the resource. The closest set of papers to our study are Budescu, Rapoport, and Suleiman (1990, 1992, 1995), Rapoport and Suleiman (1992), and Rapoport et al. (1992). In these studies, subjects make withdrawals from the resource and if the sum of withdrawals is less than or equal to the resource size, the subject receives her withdrawal. But, if the sum of withdrawals exceeds the resource size, then each subject receives nothing. The subjects make their decisions simultaneously without any communication or feedback. A robust result from the TCPR game is that an increase in threshold uncertainty leads to an increase in withdrawals. In all these studies, the number of subjects is always known with certainty.

TCPRs with Group Size Uncertainty

Despite the theoretical importance of group size uncertainty in strategic games (Myerson 1998), few studies have explored it experimentally in TCPR games. To the best of our knowledge, there are only two studies which do so: de Kwaadsteniet et al. (2008) and Au and Ngai (2003).

In Au and Ngai (2003), subjects are placed in a group and each one of them makes a withdrawal from a resource consisting of 1,000 units or “fish.” If the sum of withdrawals is less than or equal to the resource size, then the subject receives her withdrawal. Whereas if the sum of withdrawals exceeds the resource size, then each subject receives nothing. Au and Ngai (2003) analyze if the timing of withdrawals and whether uncertainty about the group size has any effect on withdrawals. They examine two withdrawal timing (or protocols of play), sequential and self-paced protocol.

In the sequential protocol, each subject in the group is assigned a position and has to make withdrawals in that order. The first subject gets to withdraw first, the second subject withdraws next, and so forth. The subjects observe the withdrawals made by those who came before them. In the self-paced protocol, the subjects are not restricted to withdraw in any prespecified order. A subject can withdraw in the first round or can wait until the next round. In each round, the subject is informed about how many other subjects have withdrawn and how much has been withdrawn.

Each protocol is played with a certain group size (five members) or an uncertain group size (the average number of group members is five, but the group size is uniformly distributed between three and seven members). In both protocols, the main finding is that withdrawals are lower under group size uncertainty, leading to a lower rate of destruction of the resource.

In de Kwaadsteneit et al. (2008), the focus is on how an individual’s social value orientation (SVO)⁵ impacts behavior in a TCPR game with group size uncertainty. They use a simultaneous protocol of play in which all players withdraw from the resource simultaneously without any communication or feedback. Our design also follows a simultaneous protocol. The key finding is that the impact of group size uncertainty on withdrawals depends on the individual’s SVO. Those subjects who are classified as pro-socials (these are more cooperative) withdraw significantly less than those who are classified as pro-selfs (these are more competitive or more individualistic) under group size uncertainty. But, when the group size is certain, then both type of subjects, pro-socials and pro-selfs, withdraw the same amount.

In both these studies, de Kwaadsteneit et al. (2008) and Au and Ngai (2003), the resource size (or the threshold) is certain and only the group size is uncertain. We now present the experimental design.

Experimental Design

There are three TCPR games and each subject participates in all three of them (within-subject design). In each of these games, the subject has to decide on how many units to withdraw from the resource. These games are followed by a risk preference elicitation task and a nonincentivized survey in which we collect demographics.

The three TCPR games are threshold uncertainty (TU), group size uncertainty (GU), and both threshold and group size uncertainty (TGU). To control for potential order effects, half the subjects first participated in the TU game, then the GU game, and finally the TGU game. While the other half of the subjects first participated in the GU game, then the TU game, and finally the TGU game. In both these orders, we kept the TGU game the final one because of its relative complexity (because in TGU, both the group size and the threshold are uncertain). In a lottery task, Moffatt, Sitzia, and Zizzo (2015) find that subjects exhibit complexity-aversion, that is, they avoid lotteries with more outcomes. However, as subjects make more decisions, complexity-aversion reduces and they become more complexity-neutral. Additionally, Dave et al. (2010) find that eliciting risk preferences through a complex task leads to noisier responses. Since the complexity of a task can potentially affect decision-making, we introduce the easier tasks (TU or GU) first in order to aid the comprehension of the more complex environment of the TGU. When subjects understand the task, they are better able to make decisions based on their preferences in changing choice environments (i.e., changes in the level of uncertainty). To further ensure comprehension, each subject took a quiz before each game and could only proceed after answering correctly.

We follow a simultaneous decision protocol (Budescu, Rapoport, and Suleiman 1995), where the subjects make each decision independently without any communication or feedback. The subjects do not know who the other group members are and cannot communicate with them. They do not receive any information about the realized value of the resource or the group size, they only know the lower and upper bound of the resource and/or group size, and that it is uniformly distributed over that range. The various levels of threshold and group size uncertainty are presented to the subjects in a different randomized order in each session. They also do not receive any feedback either about the decisions made by others or the outcome of their decisions (i.e., whether the resource is destroyed or not). We do not provide any feedback to the subjects because we want to examine how individuals respond to changes in threshold and group size uncertainty rather than how they respond to the decisions of others and past realizations of the threshold and/or group size (Camerer, Ho, and Chong 2003). Each group received an independent realization of the resource and/or group size for the randomly selected payment rounds at the end of the experiment. We now describe the TCPR games in detail (Online Supplemental Material contains experimental instructions).

Threshold Uncertainty (TU) Game

The resource is described as a box of tokens. The subjects are in a group of six members and each subject has to decide how many tokens to withdraw from the box. The exact number of tokens in the box is not known. The subjects are informed about the lower ( $α$ ) and upper bound ( $β$ ) of the number of tokens in the box and that the tokens are uniformly distributed.⁶ The mean number of tokens is always stated on their decision screen.

There are six rounds in this game (see table 1). The six rounds of the TU game are such that they allow a reasonable coverage of the threshold range (low: 10 to 70; intermediate: 250 to 450; and high: 1,400 to 1,800). Budescu, Rapoport, and Suleiman (1995) have five levels of uncertainty, but their maximum threshold range (0 to 1,000) is smaller than ours (0 to 2,000). Since we have wider range than theirs, we have more rounds.

Table 1.

Range and the Lower and Upper Bounds of the Resource Size (Tokens in the Box).

Mean Resource Size	Range (β − α)	Lower Bound (α)	Upper Bound (β)
1,000	10	995	1,005
1,000	70	965	1,035
1,000	250	875	1,125
1,000	450	775	1,225
1,000	1,400	300	1,700
1,000	1,800	100	1,900

Note: Ranges are uniformly distributed and are presented in a randomized order in each session.

Each member can withdraw any number of tokens between zero and the upper bound ( $β$ ). The subject receives the number of tokens withdrawn if the sum of withdrawals is less than or equal to the randomly drawn number of tokens (threshold) in the box. The subject receives zero tokens if the sum of withdrawals exceeds the threshold.

This payoff scheme is the same in all three TCPR games:

π_{i} = \{\begin{matrix} r_{i}, R \leq T \\ 0, R > T \end{matrix},

where $π_{i}$ is the payoff to individual i, r_i are the number of tokens withdrawn by i, R is the sum of withdrawals and T is the threshold.

Group Size Uncertainty (GU) Game

Similar to the TU game, the resource is described as tokens in a box. Here, the exact number of tokens is known (1,000 tokens). Each subject is a member of a group and has to decide how many tokens to withdraw from the box. However, the subject does not know the exact group size. The subject is informed about the lower (y) and upper bound (z) of the group size and that the group size is uniformly distributed. The mean group size is always stated on their decision screen.

There are four rounds in this game (see table 2). We restricted the GU game to four rounds because adding more rounds would have introduced potential group sizes where a social dilemma did not exist. Recall the expected group size is six, and the group size range is uniformly distributed.⁷ The widest range we have is from two to ten subjects. Two other ranges which could have been included are one to eleven subjects and zero to twelve subjects. A group size of one does not pose a social dilemma, while a group size of zero is unreasonable.

Table 2.

Range and the Lower and Upper Bounds of the Group Size.

Mean Group Size	Range (z – y)	Lower Bound (y)	Upper Bound (z)
6	8	2	10
6	6	3	9
6	4	4	8
6	2	5	7

Note: Ranges are uniformly distributed and are presented in a randomized order in each session.

Each member can withdraw any number of tokens between 0 and 1,000 tokens. If the sum of withdrawal by the group is less than or equal to 1,000 tokens, the subject receives her withdrawal. If the sum of withdrawal exceeds 1,000 tokens, the subject receives zero tokens.

Threshold and Group Size Uncertainty (TGU) Game

Similar to the TU and GU games, the resource is described as a box of tokens. The subjects are in a group and each subject has to decide how many tokens to withdraw from the box. However, the exact number of tokens in the box and the group size is unknown. The subjects are informed about the lower ( $α$ ) and upper bound ( $β$ ) of the number of tokens in the box and the lower (y) and upper bound (z) of the group size. They are informed that both the number of tokens and the group size are uniformly distributed. The mean number of tokens and the mean group size are always stated on their decision screen.

There are six different lower ( $α$ ) and upper bound ( $β$ ) of the number of tokens and the mean number of tokens is 1,000, same as the TU game (see table 1). The difference is that the group size is uncertain. We refer to low group size uncertainty (five to seven subjects) as low TGU and the high group size uncertainty (three to nine subjects) as high TGU, respectively.⁸ Since the group size uncertainty is uniformly distributed, the expected size of the group is six, the same as in the TU and GU games. We have a total of twelve rounds, the six levels of threshold uncertainty from the TU game interacted with two levels of group size uncertainty (five to seven subjects or three to nine subjects) because we wanted to examine the impact of incremental group size uncertainty (none, low, and high) and not just the binary impact of the presence or absence of group size uncertainty.

Each member can withdraw any number of tokens between zero and the upper bound ( $β$ ). If the sum of withdrawal is less than or equal to the randomly drawn number of tokens (threshold) in the box, the subject receives her withdrawal. If the sum of withdrawal exceeds the threshold, the subject receives zero tokens. We now discuss the experimental implementation.

Risk Elicitation Task

We elicit the risk preferences of the subjects using a multiple price list (MPL; Gneezy, Imas, and List 2015) in which the switch points yield a risk-preference interval identical to the Holt and Laury (2002) MPL.

In this MPL, the subjects are presented with a pair of lotteries. They choose which lottery they prefer. The first lottery is called option A while the second one is option B. In option A, the possible payoffs are 200 tokens or 160 tokens while in option B, they are 385 tokens or ten tokens. There are ten pairs in this list, and as one moves down the list, the chance of the higher payoff for both lotteries (200 and 385 tokens) increases. In the first pair, the expected value of option A is higher; in the tenth and final pair, option B gives a higher amount for sure. The pair at which the subject switches from option A to option B reveals her risk preference, with a higher switch point corresponding to higher risk aversion. Unlike other studies where a subject makes a separate choice between options A and B at each pair, subjects are asked to choose one switch point. Allowing only one switch point eliminates inconsistent responses; that is, subjects switching back and forth between options A and B. Gneezy, Imas, and List (2015) argue that enforcing a single switch point does not alter elicited parameters. One lottery is randomly selected for payment.

Payment Protocol

There are a total of four tasks in the experiment, three TCPR games (TU, GU, and TGU) and one risk preference elicitation task. There are six decisions in the TU game, four decisions in the GU game, twelve decisions in the TGU game, and ten decisions in the risk preference elicitation task. To make each task salient, one decision is randomly selected for payment from each task, giving us a total of four payment rounds.

We selected this particular procedure of paying multiple rounds for several reasons. First, it is in line with our key reference papers, increasing comparability to the prior literature (Budescu, Rapoport, and Suleiman 1995—three of the twenty trials; Botelho et al. 2014—four rounds of thirty trials). Second, it reduces the potential hypotheticality of the decisions. Finally, it helps ensure that a large portion of the sample does not walk out of the experiment with only the show-up fee and zero experimental earnings from the task (creating future recruiting problems for the lab). Nonetheless, as Cox, Sadiraj, and Schmidt (2015) point out, if subjects satisfied expected utility axioms, paying one randomly selected decision round would have been an incentive-compatible payment scheme for our experiment.

Our payment scheme raises two potential concerns. First, as the number of decisions varies between the tasks, the per-decision probability of payment also varies across tasks. It should be noted that if only one decision was to be paid, the probability would not vary, but the overall saliency would be diluted. Second, it may create portfolio effects where a subject could hedge the risk in one game with the risk in another.

Hedging for the subjects in our experiments, however, is not straightforward. Unlike a lottery choice task, where the risky and safe choices are clear, in the TCPR game, subjects face strategic uncertainty in addition to the environmental uncertainty. The presence of strategic uncertainty means that whether a choice is risky or safe will also depend on the decisions of others. Since the subjects could not communicate with others or received any feedback, they cannot be confident if the choice they make is a risky or safe one. The strategic uncertainty makes hedging more difficult. As Blanco et al. (2010) find for belief elicitation that hedging is more likely to be observed when the incentives for it are clear and obvious.

All decisions are described in tokens which are converted at the rate of twenty tokens are equal to US$1.

Hypothesis of Interest

We primarily focus on the impact of group size uncertainty on individual decisions in the presence of threshold uncertainty. We, therefore, examine whether policy makers should reduce group size uncertainty in uncertain TCPRs. Based on the findings of prior literature, the hypothesis of interest is as follows:

Hypothesis: Group size uncertainty reduces withdrawals from a TCPR with threshold uncertainty.

We now discuss the implementation details of the experiment.

Implementation

The experiment was programmed in z-Tree (Fischbacher 2007) and conducted at the Cleve E. Willis Experimental Economics Lab at the University of Massachusetts–Amherst in Fall 2017. The subjects were students of the University of Massachusetts–Amherst and recruited through ORSEE3 (Greiner 2015). There were sixty-four subjects (thirty-three females), with thirty-two subjects in each order (TU-GU-TGU and GU-TU-TGU). Each session lasted about two hours. The average earnings were US$29.71 inclusive of the US$5 show-up fee. The subjects were paid in cash and in private at the end of the session. We now present the results.

Results

Each subject participates in three experimental games (GU, TU, and TGU) and makes a total of twenty-two decisions.⁹ As we are primarily interested in the impact of group size uncertainty on withdrawal decisions in a TCPR with threshold uncertainty, our analysis is based on the behavior in the TU and TGU games. For interested readers, an analysis for the GU game is presented in Section F of Online Appendix 1. From the TU and TGU games, we have eighteen decisions per subject. There are six decisions made in each condition: TU (threshold uncertain with no group size uncertainty: six subjects), low TGU (threshold uncertainty with low group size uncertainty: five to seven subjects), and high TGU (threshold uncertainty with high group size uncertainty: three to nine subjects). In total, we have 1,152 observations (sixty-four subjects × eighteen decisions).

Individual Withdrawal Decision

An overview of the individual withdrawals is presented in figure 1. On the y-axis, for each of the conditions, we present the mean token withdrawal along with the 95 percent confidence intervals. On the x-axis, we present the range of threshold uncertainty (the difference between the upper and lower bound of the resource size). We now examine whether withdrawals differ across these conditions. Since each subject makes eighteen withdrawal decisions, the data are in panel form. Therefore, we use a random effects generalized least squares (GLS) regression in which the dependent variable is the number of tokens withdrawn (output reported in Section A of Online Appendix 1). The independent variables are dummies for group size and threshold uncertainty,¹⁰ their interaction and subject specific characteristics such as gender, risk aversion as captured by the switch point in the MPL, and a survey measure of willingness to trust others.¹¹ The regression includes a total of 1,152 observations (sixty-four subjects × eighteen withdrawal decisions: six in TU game and twelve in TGU game). There was no communication or interaction between subjects and no feedback was provided to them about their withdrawal decisions; we consider these decisions by subjects to be single-shot ones and cluster the standard errors at the individual subject level to allowing for errors to be correlated within subject.

Figure 1.

Mean tokens withdrawn.

We first examine whether withdrawals under group size uncertainty differ from when the group size is certain. The estimated differences in withdrawals are presented in figure 2. On the y-axis, we have the estimated difference in the number of tokens withdrawn along with the 95 percent confidence intervals. While on the x-axis, we have the different values for threshold uncertainty. The left panel compares the case of low group size uncertainty (five to seven subjects) with a certain group size (six subjects). Whereas the right panel compares the case of high group size uncertainty (three to nine subjects) with a certain group size. The solid line marks zero.

Figure 2.

Difference in withdrawals—uncertain versus certain group size. Note: Estimates and standard errors are presented in table D.1 in Online Appendix 1.

We see that for threshold uncertainty of 450 or less, withdrawals are significantly lower under group size uncertainty. For both low and high group size uncertainty, the estimated differences and the associated 95 percent confidence intervals are below the zero-difference line. However, when threshold uncertainty is 1,400 or more, the 95 percent confidence intervals overlap the zero-difference line. Here, group size uncertainty, either low or high, does not have a significant effect on withdrawals.

We next assess whether withdrawals are different under high and low group size uncertainty. In figure 3, the y-axis presents the estimated difference along with the 95 percent confidence intervals. The x-axis has the various values of threshold uncertainty. The solid line marks zero difference.

Figure 3.

Difference in withdrawals—high versus low group size uncertainty. Note: Estimates and standard errors are presented in table D.1 in Online Appendix 1.

Withdrawals under high group size uncertainty are significantly lower when the threshold uncertainty is 250 or less. The 95 percent intervals do not overlap the zero-difference line. However, when the threshold uncertainty is 450 or more, there is no significant difference in withdrawals. The 95 percent intervals overlap the zero-difference line. As there is greater variance in the withdrawals decisions when threshold uncertainty is 1,400 or more (see figure 1), the standard errors of the estimated differences are also higher.

The output of the GLS regression (see column 4 in table A.1 in Online Appendix 1 for the full output) shows that risk-aversion significantly reduces withdrawals. A unit increase in the safe choice in the MPL reduces withdrawals by −10.11 (p value = .021) tokens. Trusting others reduces withdrawals by −23.49 (p value = .038) tokens. While there is a negative relationship between withdrawals and being female, it is only marginally significant (p value = .083).

Overall, we find partial support for the first hypothesis: group size uncertainty reduces withdrawals in a TCPR with threshold uncertainty. The impact of group size uncertainty depends on the level of threshold uncertainty. For low levels of threshold uncertainty (450 or less), group size uncertainty significantly reduces withdrawals but not for high levels of threshold uncertainty (1,400 or more). Furthermore, for low levels of threshold uncertainty, there is a monotonic relationship between the level of group size uncertainty and the reduction in withdrawals. The higher the level of group size uncertainty, the greater the reduction in withdrawals. However, when the threshold uncertainty is high, the magnitude of group size uncertainty does not have a significant effect on withdrawals. We now have the first set of observations.

Observation 1: There is a negative relationship between withdrawals from the TCPR and group size uncertainty.

Observation 2: Threshold and group size uncertainty do not operate in isolation. Only when threshold uncertainty is low, does group size uncertainty have a significant effect on withdrawals. For high values of threshold uncertainty, withdrawals are not significantly different. Hence, the impact of group size uncertainty depends on the existing level of threshold uncertainty.

We now examine how these withdrawals impact expected earnings.¹²

Expected Group Earnings from TCPR

Unlike the withdrawal decisions, which are at the individual level, the expected earnings are analyzed at the group level. As Andreoni and Gee (2015) point out, the groups formed in the lab are only one of the many possible combinations that could have been realized. In the experiment, there is no feedback or communication or any other form of interaction. We can therefore generate pseudo-groups for the analysis (Rondeau, Poe, and Schulze 2005). For the each of the conditions—no, low or high group size uncertainty—we form a “group” by random resampling of individual withdrawal decisions. As the expected group size is six subjects, we take six individual withdrawals decision to form a “group.” We generate 1,000 pseudo-groups for the analysis.

Using an ordinary least squares regression, we examine how expected earnings vary across threshold and group size uncertainty. The dependent variable is the expected earnings while the independent variables are the threshold uncertainty, dummies for group size uncertainty, and their interaction (output reported in table E.2, Online Appendix 1).

Figure 4 presents the expected earnings from the TCPR across conditions. On the x-axis, we have the different values of the range of threshold uncertainty. On the y-axis, we have the expected earnings in tokens.

Figure 4.

Expected earnings from TCPR. Note: Estimates and standard errors are presented in table D.4 in Online Appendix 1.

A cursory inspection of figure 4 reveals that expected earnings when the group size is certain (solid line) appear to be less than when the group size is uncertain (dashed lines). Furthermore, we see that as the threshold uncertainty increases, expected earnings from the TCPR decline. The regression analysis confirms what we observe in figure 4. An increase of 100 in the range of threshold uncertainty reduces expected earnings in the certain group size condition by 11.2 tokens (p value = .000), in the low group size uncertainty condition by 23.2 tokens (p value = .000) and in the high group size uncertainty by 18.6 tokens (p value = .000).

Figure 5 shows the estimated difference in expected earnings when the group size is uncertain. In the left panel, we compare low group size uncertainty with a certain group, and in the right panel, we compare high group size uncertainty with a certain group. Figure 6 shows the estimated difference in expected earnings when the group size uncertainty is low as compared to high. In both figures, on the x-axis, we have the various values of the range of threshold uncertainty. On the y-axis, we have the estimated difference in expected earnings and the associated 95 percent confidence intervals. In both figures, we see that the estimated difference in earnings and the associated confidence intervals lie above the zero-difference line for all values of threshold uncertainty (except 1,800). This means that barring the case of extreme threshold uncertainty (1,800), expected earnings are significantly higher in the presence of group size uncertainty and are the highest when the group size uncertainty is low. We now have the final set of observations.

Figure 5.

Difference in expected earnings. Note: Estimates and standard errors are presented in table D.5 in Online Appendix 1.

Figure 6.

Difference in expected earnings—low versus high group size uncertainty. Note: Estimates and standard errors are presented in table D.5 in Online Appendix 1.

Observation 3: A reduction in threshold uncertainty increases expected earnings. The presence of group size uncertainty increases expected earnings.

Observation 4: Generally, a reduction in group size uncertainty (moving from high to low) increases expected earnings. However, if the threshold uncertainty is high, then a reduction in group size uncertainty does not have a significant effect.

Based on the preceding observations, we now discuss the policy implications of our experiment.

Policy Implications

Lab experiments can serve as an important tool to guide environmental policy-making (Palm-Forster et al. 2019). The purpose of controlled lab experiments is to help policy makers identify the impact of the variables of interest. Our study addresses the policy goal of reducing uncertainty in a common-pool resource, such as a fishery (Dankel et al. 2012). As multiple sources of uncertainty are present in a fishery (and other common-pool resources), policy makers may target one form over the other. Therefore, it is important to examine how these uncertainties might interact and necessitate a joint analysis. We explore the impact of threshold and group size uncertainty on individual withdrawal behavior. Reducing threshold uncertainty is very challenging because it emerges from the scientific nonlinearities present in environmental resources and the requisite scientific knowledge to reduce it is often lacking (Pindyck 2007; Scheffer et al. 2012). Policy makers may then seek to reduce group size uncertainty as it is relatively easier to do so. However, our results caution that eliminating group size uncertainty does not always have a desirable effect.

A potential application of our findings may be for a fishing region which is used by both commercial and recreational fishers. Suppose the number of commercial fishers is fairly stable but the number of recreational is more variable. Such a setting introduces group size uncertainty. Here, the policy makers can impose a requirement of a permit for recreational fishers and, hence, transform it to a case of group size certainty. Or they can choose an intermediate option, where they restrict recreational usage to certain days of the week. Here, the group size uncertainty is not eliminated but is reduced. Another setting where group size uncertainty might be altered by policy makers is Territorial Use Rights Fisheries (TURFs), where the government allocates the right to fish to a particular set of individuals (usually a fishing cooperative), and in theory fixing the group size and attaining group certainty (Wilen, Cancino, and Uchida 2012). However, it is possible (and quite often the case) that even those who are not members of the TURF harvest the fishery (de Geest, Stranlund, and Spraggon 2017). This creates group size uncertainty; how many poachers are there might not be known with precision. The efforts exerted in keeping poachers at bay can be conceived as altering the level of group size uncertainty. Investing heavily in defense of the TURF will reduce the number of poachers and thereby the level of group size uncertainty.

While eliminating group size uncertainty in our experiment has negative consequences, we find that reducing threshold uncertainty increases the probability of the resource surviving (see Section H of Online Appendix 1). There is some external evidence to support this result. Wilson (2002) reports that when fishermen in New England were presented with confidence intervals on recommended catch levels, they would harvest based on the upper limit of the range, rather than the average or lower end of the range. Here, the policy implication is that investing in uncertainty reduction can prove to be beneficial. The key takeaway is that when multiple sources of uncertainty exist, they might each require different policy interventions.

A major limitation of our experiment for policy makers is that the TCPR game because of its simplicity, small group size, and low stakes cannot directly help devise policy prescriptions for complex, large-scale, and high-value common-pool resources such as fisheries. Rather the benefit of small experiments such as ours is to provide indicative evidence. For instance, take the case of experimental climate change games which identify threshold uncertainty as an obstacle to coordinating efforts to tackle climate change (Barret and Dannenberg 2012; Dannenberg et al. 2015; Brown and Kroll 2017). While these games cannot capture the complex details of reaching an international agreement on climate change, they remain useful to policy makers because their findings draw attention to the potential problems caused by and implications of the presence of threshold uncertainty. We now turn to the closing discussion.

Closing Discussion

Overharvesting poses a serious challenge to the sustainable use of common-pool resources. Policy makers therefore are interested in better understanding the determinants of harvesting decisions. We design an experiment to examine individual withdrawal behavior under uncertainty in a TCPR. These resources can be used sustainably up to the threshold, but consumption beyond the threshold leads to its destruction. Earlier work has analyzed the impact of threshold uncertainty (not knowing the exact size of the resource) and group size uncertainty (not knowing the exact number of resource users) but in isolation (threshold uncertainty with a certain group size or a certain threshold with an uncertain group size).

Our key contribution is to examine threshold and group size uncertainty jointly. Evaluating their joint impact is important because they appear simultaneously in real-world settings. Overall, we find that the presence of group size uncertainty reduces withdrawals, increases the likelihood of the resource surviving, and leads to higher expected earnings. While an increase in threshold uncertainty increases, the chance of the resource being destroyed and reduces expected earnings.

The key policy insight is that a one-size-fits-all policy toward uncertainty in common-pool resources is inadequate. Policy makers should account for the differential impact of threshold and group size uncertainty as well as the interaction between them. While reducing threshold uncertainty should be a priority for policy makers, the case of group size uncertainty requires a more nuanced approach.

Policy makers seeking to maximize expected earnings from the resource should strive to reduce threshold uncertainty. Group size uncertainty, both low and high, significantly increases expected earnings except for when threshold uncertainty is very high. Reducing group size uncertainty from high to low further increases expected earnings. Complete elimination of group size uncertainty may be counterproductive as expected earnings are the lowest when the group size is certain.

While this study has addressed an important gap in the literature on behavior in uncertain social dilemmas, further examination of this topic is warranted given the important policy implications of this line of research (Van Lange et al. 2013). Future scholars can investigate whether these results hold for larger groups, under ambiguity as opposed to risk, in a dynamic setting instead of a static framework, when monitoring and sanctioning technologies are available, if there is partial and not full destruction of the resource among others.

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Footnotes

Authors’ Note

The funding source did not play any role in determining the study design or the analysis of the data. The opinions expressed here do not reflect the views of the funder. Abdul H. Kidwai is now affiliated with Department of Economics, University of Wisconsin - La Crosse.

Acknowledgments

The authors thank John Spraggon, Simon Halliday, Irene Mussio, Mehak Kaushik, Emma Grazier, and Scott Cohn for their input. They would also like to thank the participants at the Canadian Economic Association 2018 meeting and New England Experimental Economics Workshop 2019 for their comments.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work was supported by the Center for Behavioral and Experimental Agri-Environmental Research (Grant No. S19000000000495).

ORCID iD

Abdul H. Kidwai

Supplemental Material

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Notes

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