Abundance of Resources and Incentives for Collusion in Fisheries

Abstract

The aim of this study is to explore theoretically the circumstances in which collusion can emerge between artisanal organizations and external agents. We also analyze theoretically how collusion can alter the sustainability equilibria of marine resources. In situations of incomplete information where external agents are not aware of the initial stock of resources, we observe how those agents decide whether to accept or reject offers of collusion from artisanal organizations. We find that collusion is more likely to occur when the resource is abundant than when resources are scarce, as in the latter case, the external consultant has to be more careful with the established quota so as not to deplete the resource. Further, we find that organizations are more impatient in proposing collusion when the resources are scarce.

1. Introduction

The misuse of open resources by selfish economic agents is a classic economic problem known as the tragedy of the commons. In the case of fisheries, over-fishing can cause the system to collapse, leaving society worse off because of the uncoordinated use of resources by rent-seeking agents. One possible solution for the misuse of resources is to restrict access, that is, grant collective rights. The Territorial Use Right for Fishing (TURF) allocates to groups secure and exclusive harvesting rights to fish one or more marine species in a specific area. The aim of the TURF is to control fishers and hold them accountable for their use of common pool resources [1,2,3]. Even though the use of TURFs can reduce and monitor the misuse of common resources, collusion (not cooperation) among fishers and external agents, such as consultants or inspectors, may promote over-catching and, ultimately, depletion of resources.

It is relevant then to define and distinguish between collusion and cooperation. First, according to [4], collusion refers to combinations, conspiracies, or agreements among sellers to raise or fix prices and to reduce output in order to increase profits, whereas according to [5], cooperation in the economic tradition is mutual assistance between egoists’ agents. Then it is clear that collusion seems to be related to an intention to deceive others; meanwhile, cooperation refers to joint help.

Given these interactions between agents, the relationships between different types of agents are involved in managing common property of natural resources. For example, the authors of [6] argue that to understand the dynamics between agents in common pool resources (CPR), it is necessary to consider their horizontal and vertical relationships. These horizontal and vertical interactions could influence the behavior of agents when they attempt to maximize their profits. Furthermore, according to [7], possible collusion between agents can result in management and implementation failures in that collusion makes it more likely for fishery regulators to approve total allowable catches greater than those recommended by scientists (that is, management failure). Collusion can also entice fish monitors to deliberately allow fishers to catch more than their approved quotas (that is, implementation failure). In our article, we define collusion as an agreement between two different agents to extract a higher level of resources, which is detrimental to resource abundance and sustainability objectives. Agents may choose to participate in collusion because of incentives to maximize personal rents, even at the cost of social welfare.

To avoid over-catching, the government usually establishes a quota that ensures the sustainability of common pool resources. This quota should prevent fishers from over-exploiting resources; however, empirical evidence suggests that quotas established by external consultants can be altered through collusion between fishers and consultants, ultimately leading to a depletion of resources. For example, the authors of [7] argue that collusion can negate efforts to end over-fishing or rebuild fish stocks. A consequence of collusion, then, is the use or overuse of community natural resources with the consent of an external agent—overuse that could alter the quota. This implies that in the official report, fishing communities are extracting quantities less than or equal to that allowed by the quota, but that the quota is over the scientifically recommended level of extraction.

Incentives for collusion are increasing, as indicated by [8,9]. With resources becoming scarcer and access to those resources becoming more valuable, incentives for corrupt practices (such as collusion) are bound to increase. For example, bribery is prevalent between fishery officials and fishers [10,11]. On the other hand, despite evidence showing the positive biological and economic effects of TURFs, there is actually a lack of knowledge about the key factors that affect marine resources’ sustainability. Therefore, we contribute to this line of inquiry by analyzing how the relationship between agents, fishers, and external agents could be corrupted by collusion. (The external agent could be an inspector or a consultant who assesses the abundance of the resource).

The aim of this paper is to strategically analyze the interaction between fishers represented by an artisanal organization and external agents when there could be incentives for collusion in their relationship. In other words, we analyze how collusion can alter the sustainability equilibrium of the system and offer useful pathways to develop effective policies. Even externalities can be internalized—fishers may have an incentive to exceed sustainable limits if the resource is scarce or when they are “impatient” about future payments. These are the hypotheses explored in this paper.

The principal–agent framework can be used to analyze the interaction between fishers and external agents. Artisanal fisher organizations are better informed about the state of resource stocks than external agents, but the external agents have to establish a quota—a quota the organizations must comply with. Given this situation, collusion can emerge if the organization wants to exceed the given quota to maximize profits.

Our baseline model examines a setting in which the external agent is not familiar with current resource levels; that is, they are less informed than the artisanal organization. This scenario could lead to a number of outcomes. For example, the artisanal organization could propose colluding with the external agent if resources are scarce, and the external agent could interpret that offer as an indicator of resource stock and act accordingly. We analyze the structure of this interaction by considering the relationship between agents in two different static scenarios: with complete and incomplete information. We also analyze an extension with a dynamic structure.

In one of the static models, we assume the external agent has incomplete information. With incomplete information, the external agent, upon observing a collusion offer from the artisanal organization, cannot determine whether the current resource stock is high or low. Even without this information, they must decide to accept or reject the offer to collude. In this scenario, the game follows this path: first, nature determines the stock of the resource (high or low); the artisanal organization privately observes that state and chooses to offer collusion, C, or not offer collusion, $NC$. Second, the external agent is not aware of the resource’s stock; however, they must decide to either accept the collusion, A, or reject the collusion, R.

We found that two types of equilibrium can be achieved. Each type depends on the probability that the resource stock is high. In the first scenario, the external consultant rejects colluding, assuming that stock is high, independent of the artisanal organization’s strategy. In the second scenario, the external consultant can accept or reject collusion depending on the strategy of the artisanal organization with a higher probability of having abundant resources. We extend our model into two periods, which functions as a robustness check of the previous results. Finally, we determine a patience value for artisanal organizations, finding that organizations are more impatient when resources are scare.

The organization of the paper is as follow: a literature review is presented in the next section. Then, the model setup is described, followed by the equilibrium analysis of both the static and the dynamic model. Section 5 presents a dynamic extension of the model. Finally, discussions and conclusions are drawn.

2. Related Literature

Common pool resource (CPR) problems have been extensively studied. The exploitation of open resources is the main concern in this literature. For example, the tragedy of the commons provides a framework for understanding the consequences of over-exploitation of open resources [12]. The effects of noncooperation between agents in the use of common pool resources has been recognized in the literature and in practice. For example, the authors of [13] explain that in 1993, many fish stocks in Canada were close to collapse. He found that the Canadian northern cod was so scarce that the fishery needed to be closed; [14,15] analyses how firms react to different penalties from regulators; and [16] describes how illegal catching impacts quota decisions. In Europe, quotas have been cut significantly to reduce over-fishing. More recently, ref. [17] found that for 13 of the 20 most common species in Madagascar, fishing mortality exceeds natural mortality. Moreover, over-fishing in western Madagascar presents a serious threat to the income, food security, and well-being of some of the most vulnerable people in the world, and [18] concludes that actor behavior is important for policy interventions in research based on small-scale fisheries in Kenya.

On the other hand, some researchers argue that sustainable extraction behavior and responsible use of resources can be maintained when harvesting activities are cooperative [19,20,21]. As a result, some alternative regimes have been implemented to foster both the recovery of fisheries and more-sustainable activities for the future. The two regimes most commonly mentioned in the literature are the individual transferable fishing quotas system (ITQs) and the territorial use rights for fisheries (TURFs), which grant rights to a group of individuals [1,22,23].

As expected from previous international experiences, the TURFs regime has allowed resource recovery while also making artisanal fishery a more sustainable activity [1,24]. Despite evidence indicating the positive biological and economic effects of implementing TURFs, there is a lack of knowledge about the key factors affecting the operation of fishers’ organizations within this system. In addition, in methodological terms, ref. [21] highlights the importance of conducting analyses beyond the perceptions of fishers and involving biological, economic, and social dimensions in a multidimensional approach rather than as a separate analysis. We contribute to this call by using a principal–agent model analyzing possible collusion between artisanal organizations and external agents.

The purpose of the TURF management system is to provide incentives for organization members to sustainably exploit resources in a given area, thus avoiding resource depletion [25]. However, corrupt practices within the TURF system, such as illegal fishing, collusion, and over-fishing, have been documented in several countries around the world, including Malaysia, Chile, and South Africa [21].

According to [1], scientific information such as resource health and stock status plays an essential role in managing TURFs because this information is gathered and disseminated via partnerships between TURFs and the federal agencies (external agents) responsible for overseeing the TURFs. Given the importance of the relationship between these two entities on the sustainability of marine resources, we have included it in our analysis to determine how the initial stock of resources can affect this relationship and potentially steer the relationship towards practices that risk future resource sustainability.

Another key element in the operation of the TURFs that has an impact on the sustainability of the resource is the inspections or controls that are carried out in TURF management areas. For example, ref. [26] argues that poaching within fishery management areas in Chile has increased in recent years, affecting the sustainability of resources; Ref. [27] studied the management of CPR in developing countries, and their results show high levels of irregularity in inspectors who manage common resources, thus contributing to the over-exploitation of fishing. These authors included bribing inspectors to overlook over-exploitation as a point of analysis. We incorporate bribing in our theoretical model, where one of the roles that the external agent can have is as an inspector who can receive a bribe to change his/her reports.

Another paper related to corrupt practices in fisheries is [28]. They explore corruption practices in global fisheries. They argue that despite its importance, effective management, and hence the sustainability of the sector, is often threatened by corruption. They found evidence of corruption in many ways, for example, in licensing. They also present evidence of poor enforcement of rules and regulations and occasional bribery and extortion in the monitoring and inspection of catches and supply chains. In addition, ref. [29] recognize the impact of resource rents. When leasing a portion of their rents, organizations spend time and energy looking for renters instead of utilizing their time and abilities more productively. As a consequence, collusion and other kinds of corruption are the principal motivation behind why resource-rich nations perform poorly in economic terms. The authors’ main conclusion is that policy makers should focus more on the performance of these kinds of organizations (related to resource extraction) and how they could work more efficiently. Considering these conclusions, we better understand how fishers seeking to maximize their profit might adapt their strategies as the probability of resource abundance changes.

A paper closely related to this is [10]. The author argues that the literature on compliance behavior in fisheries has largely ignored the effect of corruption within the authorities responsible for enforcing fishery regulations. Moreover, he examines the effect of corruptibility of the enforcing authority empirically using scenario experiments with South African small-scale fishermen. The main findings are that perceived corruptibility of authorities corrodes willingness to comply with regulations. Both grand and petty types of corruption have significant effects. Similar to [10], we are interested in analyzing the corruption between authorities and fisheries; however, there are significant differences between our studies. First, we use a game theory approach to analyze the interaction between agents. Second, we study both the biological and economic consequences of collusion between agents. Additionally, some researchers claim that in many cases, as the scarcity of a resource increases, common property regulation (i.e., through quotas) tends to be less efficient, and there is an increased likelihood that some users will ignore regulations [30]. Therefore, we consider the abundance of the resource as a key variable to motivate corrupt practices between TURFs and consultants.

Finally, given the structure of our model, where there is asymmetric information between players, our study is related to [31]. As [31] states, there are several ways to apply the principal–agent problem to fisheries, including through share contracts, international fishing agreements, illegal landings, etc. However, little is known about the principal–agent problem between artisanal fisheries and external consultants.

In the following sections, we first examine the complete information setting as a benchmark and then focus on the incomplete information context.

3. Model

The following model can be embedded in a principal–agent structure, where the artisanal organization is the agent, and the external agent is the principal; that is, the artisanal organization is better informed about the existing abundance of the resource than the external agent, but the external agent has to establish/control a quota—a quota that the organization must comply with. In other words, since there is asymmetric information regarding the state of the resource, a principal–agent situation emerges. Given this, collusion can emerge if the organization wants to exceed the quota because of the current state of resource stock. In order to analyze whether collusion occurs, consider a collusion game with two players: an artisanal organization ($AO$) and an external agent ($EA$). The initial stock is exogenously given, ${\theta }_k$, where $k=\{H,L\}$, and it can be high/abundant, ${\theta }_H$, with a probability p, or low/scarce, ${\theta }_L$, with a probability $(1-p)$. In the first instance, the initial stock is observed by $AO$ but not by $EA$. The artisanal organization extracts an amount $q_m\in [0,1]$ with $m=\{i,j\}$, where $q_i$ denotes legal extraction and $q_j$ extra/illegal extraction. Then, $AO$’s and $EA$’s profit extraction, following [32], without collusion is

$${\pi }_{AO}^{NC}=q_i-\frac{q_i^2}{{\theta }_k},\mathrm{and}{\pi }_{EA}^{NC}=W$$

(1)

where the first term in $AO$’s payoff represents the revenue with the price of fishing normalized to one. The second term shows the fishing cost, which increases with artisanal organization extraction and decreases with the abundance of the stock. $EA$’s profit without corruption represents his/her standard salary for expert services.

If the artisanal organization offers to collude (corruption action), it can be accepted, A, or rejected, R, by the external agent. Therefore, if $EA$ chooses reject, the respective payoffs are

$${\pi }_{AO}^{C,R}=q_i-\frac{q_i^2}{{\theta }_k}-S,\mathrm{and}{\pi }_{EA}^{C,R}=W$$

(2)

The first two terms in $AO$’s payoff function are the same as those shown in Equation (1), but the third term represent the sanction received by an authority for offering to collude with $EA$. Further, the payoff for $EA$ is the same as in Equation (1) because he/she did not accept the collusion. On the other hand, if the collusion offer is accepted by $AC$, payoffs are as follow

$${\pi }_{AO}^{C,A}=(q_i+q_j)-\frac{1}{{\theta }_k}\left[q_i^2+q_j^2(1+\beta )\right],\mathrm{and}{\pi }_{EA}^{C,A}=W+\beta \frac{q_j^2}{{\theta }_k}-c_k$$

(3)

where the first term in brackets shows the total revenue, i.e., the extraction according to resource abundance, $q_i$, and the additional extraction coming from the accepted collusion, $q_j$. The second term defines the total cost, which is composed of the extraction cost and bribery paid to $EA$. That bribery is a function of the additional quota approved. Furthermore, for $EA$, payoff is composed of the salary, W, the bribery received, $\beta \frac{q_j^2}{{\theta }_k}$, and a personal cost, $c_k$, which depends on the state of the stock. If the state of the resource is high, the cost is less than the bribery received, $c_H<\beta \frac{q_j^2}{{\theta }_H}$, representing for $EA$ that increasing the quota when the resource is high is less damaging than increasing the quota when the resource is low. If the state is low, the cost is greater than the bribery received, $c_L>\beta \frac{q_j^2}{{\theta }_L}$; increasing the quota more than necessary is costly for the consultant because the resource is scarce.

The time structure of the game is as follows:

1.

Nature selects the state of the resource: high, H, or low, L.

2.

The artisanal organization, $AO$, privately observes the state of the resource and chooses to collude, C, or not to collude, $NC$.

3.

The external agent, $EA$, does not know the state of the stock. However, they must decide to accept the collusion, A, or reject the collusion, R.

The next lemma presents the equilibrium behavior in the complete-information version of the game where the $EA$ can perfectly observe the state of resource stock.

Lemma 1.

With complete information when the resource stock is high, the Nash equilibrium is $\{C,A\}$. Meanwhile, when the resource stock is low, the Nash equilibrium is $\{NC,R\}$.

The lemma above establishes the effect of resource stock on collusion when players have complete information. If the stock is high and players encounter resource abundance, then the equilibrium is one in which collusion is proposed and accepted. On the contrary, if the stock is low, players face a scarcity of the resource, and the equilibrium is one in which collusion is not proposed. This is because when stock is low, it is costly for the external agent to accept the collusion, and the artisanal organization anticipates that strategy; therefore, $AO$ prefers not to offer collusion.

This is an interesting result because even though scarce resources create incentives for fishers to propose alterations to the established quota (which, according to our results above, occurs), the external agent rejects collusion because accepting may cause depletion of the resource. Hence, collusion is more likely to occur when resources are abundant. Next, we compare our equilibrium results with complete information against the presence of asymmetric information between $AO$ and $EC$, as the following section shows.

4. Equilibrium Analysis

In this section, we study how our results above are affected by incomplete information, where nature determines the level of stock, either high or low, with probabilities p and $1-p$, respectively. Observing that state, $AO$ chooses between colluding, C, and not colluding, $NC$. Finally, $EA$ is not aware of the resource stock and responds A or R. Next, we discuss the Perfect Bayesian Equilibrium (PBE) results of the incomplete information game. (Figure A1 in Appendix A provides a graphical representation of the game).

Proposition 1.

With incomplete information, the following Perfect Bayesian Equilibrium can emerge:

1.

In the first case, the artisanal organization chooses $\{C-C^{\prime }\}$ if $\beta <\widehat{\beta }$, where $\widehat{\beta }\equiv \frac{{\theta }_k-q_j}{q_j}$, where $k\in \{H,L\}$, and the external agent selects A, if and only if $p<\tilde{p}$, where $\tilde{p}\equiv \frac{{\theta }_H{\theta }_L{C}_2-{\theta }_H\beta q_j^2}{\beta q_j^2({\theta }_L-{\theta }_H)-{\theta }_L{\theta }_H(C_2-C_1)}$.

2.

In the second case, the artisanal organization chooses $\{NC-N{C}^{\prime }\}$, and the external agent selects R.

Proposition 1 establishes two types of equilibria. In the first one, the artisanal organization is insensitive to the resource’s stock, p; this means that $AO$ chooses to collude regardless of the probability of a certain state of nature, high or low, if $EA$ chooses to accept, A. However, for the external agent, this situation is different. His/her response depends on the probability, p, and there is a threshold in his/her responses. On the one hand, the external agent accepts the offer when the probability of abundance of the resource, p, is lower than $\tilde{p}$. On the other hand, the external agent rejects the collusion offered. The second equilibrium entails non-collusion regardless of the resource stock when $AO$ anticipates that $EA$ will reject the offer.

This result suggests that when the probability of an abundant stock is low, less than $\tilde{p}$, the equilibrium of the game is given by non-collusion between the agents, as stated before. However, when the probability of abundance is high, i.e., p greater than $\tilde{p}$, collusion become a sustainable strategy.

In this incomplete information scenario, players behave similarly to those in the complete information scenario. The $EA$’s inability to observe the state of the stock leads to a cautious response by artisanal organizations. Because $EA$ chooses R under a wide range of p, $AO$ leans toward choosing $NC$. Intuitively, if the artisanal organization proposes collusion, the external agent can infer a low level of stock and hence reject the collusion. This forces $AO$ to be cautious with their offer because being rejected could entail the extra cost of a sanction.

Since in the first PBE, $AO$ chooses the strategy $\{C,C^{\prime }\}$ if and only if $\beta <\left(\frac{{\theta }_k-q_j}{q_j}\right)$, that means collusion occurs only if the bribe $\beta$ is sufficiently lower than the percentage of the illegal quota $q_j$. In other words, if the amount of the bribe is excessively high, then the illegal quota is not worth it. For that reason, $AO$ chooses to collude if the bribe for that collusion is lower than the percentage of extra quota, measured by the ratio between the stock of the resource and the additional quota gained from the bribe. (A similar result holds if $EA$ receives payment or reward for rejecting the collusion offer, which would lead to an increase in bribery to reach an agreement between agents. This means that the new bribe should be at least equal to the cost and the reward, $\beta \frac{q_j}{{\theta }_k}=c_k+reward$, for an agreement to be made).

The restriction from the first PBE, $\beta <\left(\frac{{\theta }_k-q_j}{q_j}\right)$, can be rearranged as $\beta \frac{q_2^2}{{\theta }_k}<\left(1-\frac{q_2}{{\theta }_k}\right)q_2$, where the left side represents the bribe paid by $AO$ and the right side indicates the growth of the extra quota in relation to the total size of stock. This means that the amount of the bribe should grow more slowly than the relation between the additional quota and the total stock; otherwise, paying the bribe is not profitable for the artisanal organization.

Proposition 2.

A total quota Q does not guarantee sustainability resources if there is a positive illegal quota $q_j>0$ and $q_i^{*}={\theta }_k/2$, which represents the maximum sustainable yield for $AO$ exceeding $Q\le q_i+q_j$. A total quota Q guarantees sustainability of resources if there is an illegal quota $q_j<{\theta }_k/2$ and $q_i<q_j$, including if $Q\le q_i+q_j$.

The proposition above can be explained visually in the following figure, where the graph on the left represents guaranteed stock sustainability, and the graph on the right shows non-guaranteed stock sustainability.

First, let us observe the left graph. Knowing that there is an illegal positive quota $q_2$, sustainability of resources can be guaranteed if $Q=q_i+q_j\le {\theta }_k/2$. In other words, an illegal quota can be extracted and the resource can still be guaranteed as long as optimal conditions hold, as we can see on the left graph. In the second case (the right graph), we can observe that if the illegal quota exceeds the optimal condition of Q, then resource sustainability cannot be guaranteed in the next period. Given this, policies implemented to avoid illegal catching can be mismatched since sustainable equilibrium can be maintained even with illegal catching.

5. Dynamic Extension

We now extend the base model from Section 3 into two periods in order to analyze the robustness of the equilibria found before and to identify possible inefficiencies produced by collusion. In this extended game, agents can observe what happened in the first period before they choose their strategies for the second one. (The uncertainty in the stock for the second period disappears, since the stock of the second period is understood as a consequence of the actions of the first period. The function for the second period stock appears in Equation (4) and is explained in the following paragraph). In the second period, the artisanal organization extracts an amount $x_m\in [0,1]$, where $m=\{i,j\}$; therefore, $x_i$ and $x_j$ represent the legal and illegal (coming from collusion) quotas for extraction, respectively. (Figure A2 in Appendix A provides a graphical representation of the game). Then, $AO$’s and $EA$’s extraction without collusion is

$${\pi }_{2,AO}^{NC}=x_i-\frac{x_i^2}{{\theta }_k(1+g)-Q},\mathrm{and}{\pi }_{2,EC}^{NC}=W.$$

(4)

where a subscript “2” is added in the profit function to denote the second period’s profit, while $Q=q_i+q_j$ represents first period’s aggregate appropriation. Note that the available stock at the beginning of the second period is ${\theta }_k(1+g)-Q$, and $g\in [0,Q/{\theta }_k]$, which represents the growth rate of the initial stock. When $g=0$, the initial stock does not grow, implying that fishers encounter a stock of ${\theta }_k-Q$ at the beginning of the second period. In contrast, when $g=Q/{\theta }_k$, the stock is fully recovered, so the initial stock, ${\theta }_k$, is available again at the beginning of the second period.

Hence, second-period profits when artisanal organizations offer to collude and $EA$ chooses to reject are

$${\pi }_{2,AO}^{C,R}=x_i-\frac{x_i^2}{{\theta }_k(1+g)-Q}-S,\mathrm{and}{\pi }_{2,EA}^{C,R}=W.$$

(5)

which are analogous to first-period profits, and, for simplicity, the sanction when collusion is offered but rejected is the same as that of the first period. However, if the collusion offer is accepted by $EA$, payoffs are as follows

$${\pi }_{2,AO}^{C,A}=(x_i+x_j)-\frac{\left[x_i^2+x_j^2(1+\gamma )\right]}{{\theta }_k(1+g)-Q},\mathrm{and}{\pi }_{EA}^{C,A}=W+\gamma \frac{x_j^2}{{\theta }_k(1+g)-Q}-c_k.$$

(6)

Equation (6) is similar to Equation (3); this means that the first term in brackets shows the total revenue, and the second term defines the total cost by $EA$, where now bribery is denoted by $\gamma \frac{x_2^2}{{\theta }_k(1+g)-Q}$. Additionally for $EA$, the payoff is composed of the salary, W, the bribery, and a cost, $c_k$, which now depends on the state of the stock at the beginning of the game.

Solving the game by backward induction, we obtain the same Perfect Bayesian Equilibrium as in Proposition 1, which represents a robustness check of the previous results. The following Lemma summarizes the results for the dynamic version:

Lemma 2.

With incomplete information, the PBE found for the dynamic game is the same as that found for Proposition 1. In addition, the second-period equilibrium satisfies $\{C^2,A^2\}$ if ${\theta }_k={\theta }_H$, and $\{N{C}^2,R^2\}$ if ${\theta }_k={\theta }_L$, where superscript denotes the strategies corresponding to the second period.

Since agents in the second period have complete information, they can anticipate the respective strategies and bring their payoffs from the end of the first period, where they were uncertain of the initial stock. Solving the game, we find that the equilibrium depends both on the bribe paid and on probability p, which indicates the abundance of the stock. These results are consistent with those found in the base model.

Results for the second period are consistent with the benchmark model, indicating that collusion occurs in cases of stock abundance. This is because the external agent is sensitive to the abundance of the resource, which is one of the assumptions of the model in Section 3. In any other case, collusion would be present regardless of the abundance of the resource.

While these results identify the presence of inefficiencies in each scenario, we compare these inefficiencies produced between the model in its static version—one period—and its dynamic version—two periods. (Inefficiency is understood as the difference between extraction without collusion, which is used as the benchmark, and extraction when collusion is present). The following corollary shows relationships between these inefficiencies across the time versions and with complete information.

Corollary 1.

With complete information, static and dynamic models satisfy $q_1^s>q_1^d$ and $q_2^s>q_2^d$, where $\{s,d\}$ represents the static and dynamic versions, respectively.

In the static model, a quota from collusion is greater than in the dynamic model; this applies to both the first and second periods. Hence, extraction during one period and at the aggregate level (both periods) is larger under a static model. This means that artisanal organizations working under a single-period model tend toward more intense over-exploitation of resources, increasing the likelihood of unsustainable resource management. This situation is represented by the interval to the left of the point of sustainability shown in Figure 1a. The greater the over-exploitation, the further to the left the resource will be found.

The dynamic version, on the other hand, internalizes the increasing over-exploitation of the stock. In other words, the presence of both periods in the model helps correct/reduce the inefficiencies from over-exploitation that one single period would not have been able to correct on its own.

Moreover, given the structure of the game, we can compare agent patience using the discount factor, $\delta$, on different equilibria. Comparing two specific equilibria of the complete information game, $\{N{C}^1;N{C}^2\}$ and $\{C^1,A^1;C^2,A^2\}$, we can establish the following corollary:

Corollary 2.

With complete information, organizations are more patient in equilibria with no collusion compared to equilibria with collusion, as long as $q_1>\theta /2$.

This is an interesting result because organizations shows a larger discount factor, $\delta$, in equilibrium types $N{C}^1;N{C}^2$ (no collusion) than in types $C^1,A^1;C^2,A^2$ (collusion). One reason to explain this is that the organization would not propose a collusion unless it is necessary, i.e., when resources are already scarce. Thus, organizations will be more impatient in equilibria where collusion is present.

6. Discussion and Conclusions

This paper examines how collusion can arise between an artisanal organization and an external agent. External agents include inspectors, who are legal authorities (vertical collusion), and external consultants (horizontal collusion). We first examine a complete information model as a benchmark. Then, we solve the same game using an incomplete information model, where $AO$ is better informed than $EC$. Finally, we extend the model to a dynamic setting where the agents interact during two periods.

Our results in Section 3 suggest that collusion can only occur when the initial resource stock is high. Policy can be focused around reducing collusion when there are abundant natural resources. On the contrary, when resources are scarce, collusion with the external consultant is less likely to occur due to scarcity. The mechanism at play is that when resources are scarce, the external consultants have to be more careful in setting the quota than they do when resources are high.

In Section 4, in Proposition 1, our results suggest that the expert consultant can infer low resource stock if the organization proposes collusion. In Proposition 2, our results suggest that there can be illegal catching without exceeding the biological limit; that is, illegal quotas can still be found in sustainable environments. This information is relevant for policymakers who tend to consider the legal quota as the maximum sustainable limit.

Another important aspect presented in this paper is that the behavior of organizations is determined partly by of the scarcity (or abundance) of resources. For example, in the two-period and complete information scenarios, organizations are more patient in proposing collusion when resources are abundant. This can have interesting policy implications because we can observe specific scenarios in which collusion occurs.

The abundance of resources tends to make common-property regulation by quotas less efficient, and it also increases the probability of collusion between some agents, such as fishers and artisanal organization on the one side and inspectors and external consultant on the other side. Therefore, efficiency losses resulting from externalities increase with the value of the resource.

The original design of the TURFs system assumed that organizations would manage all issues related to the area, including quotas. This is an ideal scenario for regulators because enforcement is costly. However, in practice, organizations share management responsibilities with regulators: external consultants determine environmentally friendly quotas, and inspectors regulate enforcement of these quotas. What, then, is the preferable role for artisanal organizations and regulators in terms of increasing sustainability? Regulators should increase penalties for agents involved in bad practices such as collusion.

Given these findings, it would be interesting to explore in depth a conceptual analysis of this paper with empirical work. While it is difficult to obtain empirical data, experimental economics can be a useful tool for studying human behavior in a controlled laboratory setting or in the field. Such a methodology could test the theoretical models developed in this paper.

Our results beg the question: Who monitors the monitors? Some researchers, such as [33,34], among other, have already explored this issue. Although those studies are applied in other contexts, they highlight the importance of monitoring the regulators because of existing biases favoring regulators’ preferences. Therefore, it would be interesting to analyze situations in which relationships between an artisanal organization and an external agent include a supervisor.