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Game Theoretical Models of Effort and Lobbying in a Heterogeneous CPR Setting Matthew Freeman Louisiana State University/LA Sea Grant Chris Anderson University of Rhode Island

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Effort & Lobbying Extraction from a common pool resource (CPR), such as a fishery, can lead to socially inefficient and undesirable outcomes. Through regulation of the CPR, users may achieve a more profitable and socially efficient outcome. However, assumptions made by traditional CPR models provide an incomplete framework to guide fishery policy.

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Research Question Motivating Question – As the assumptions that CPR users (1) are homogeneous and (2) are unable to create, or influence, management of the resource are relaxed, what do theoretical models predict? – In particular, we examine heterogeneity in the cost function of CPR users and the influence of CPR users on proposed regulation of the resource.

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Outline of Model Presentations We present the game-theoretical models and Nash equilibrium strategies so that we build upon the preceding model by either incorporating an additional element or displaying a unique case. In doing so, we solve for an unregulated CPR, several cases for a regulated CPR, and several cases in which lobbying occurs in a regulated CPR.

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Theoretical Symbols & Equations

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(1) Unregulated CPR Model

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Model Details When δ A >δ B, the Nash equilibrium choice of individuals in Group A is < that of individuals in Group B. Group B’s aggregate effort, however, could be >, <, or = to that of Group A’s, dependent on the number of individuals in each group. Interpreting δ A >δ B as the difference in the externality cost experienced by small and large vessel operators, we could expect large vessel operators to exert more effort than small vessel operators in a CPR, based on the Nash equilibrium predictions.

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(2) Regulated Models Next, our model incorporates regulation to limit the appropriation level of individuals, and uses one of the allocation rules discussed by Hackett (1992), whereby appropriation rights are equally divided. For fisheries, this could take the form of equal share quotas, or daily or weekly trip limits.

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(2A) Regulated CPR Model – Industry Social Optimum

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Model Details In the solution, we observe in the denominator both the number of individuals in each group and the externality cost experienced by them. As a result, if either an externality cost increases or a group size increases, the socially optimal regulation decreases.

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(2B) Regulated CPR Model – Nash Equilibrium Both groups of individuals have the opportunity to choose their Nash equilibrium effort levels when, and both groups of individuals would choose when. Thus, we are left to determine the effort levels that occur when.

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Regulated CPR Model – Nash Equilibrium However, there’s a level of effort where individuals from Group A become bound by the constraint, and must select the cap for an effort level.

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Regulated CPR Model – Nash Equilibrium

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We have a unique solution wherein Group A individuals are exceeding their unregulated Nash equilibrium, since Group B individuals are prevented from selecting their unregulated NE. (The best response function of Group A individuals has been altered due to the constraint of the regulation on Group B individuals.)

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(2C) Regulated CPR Model – Group Preferred Regulation This model becomes useful in our next step – where CPR users lobby according to their group preferred regulation.

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(3) Regulated CPR Model – Non-Cooperative Lobbying This model requires backward induction by the CPR users: CPR users must first determine the optimal final regulation and then determine the level of lobbying required, given the proposed regulation.

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Regulated CPR Model – Non-Cooperative Lobbying Lobbying expenditures to increase a proposed regulation are as follows: When δ A > δ B, we note (1) the preferred regulation for Group A is smaller than for Group B and (2) the region about the preferred regulation in which lobbying is unprofitable is smaller for Group A than for Group B. This is the group preferred regulation that was previously identified. This helps to determine the “lower bound” for profitable lobbying.

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Regulated CPR Model – Non-Cooperative Lobbying Based on where the ‘lower limit’ of profitable lobbying occurs, one group’s NE may be to not spend any money lobbying & to free-ride on the other group’s activities.

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(3) Regulated CPR Model – Non-Cooperative Lobbying To decrease a proposed regulation, we simply examine only ‘negative’ lobbying expenditures, whereas before we examined ‘positive’ lobbying expenditures in the constraint.

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Regulated CPR Model – Non-Cooperative Lobbying Lobbying expenditures to decrease a proposed regulation are as follows: A boundary does exist where an individual would NOT want to lobby using these equations. So, an individual would want to compare the profit earned at his respective upper bound (minus any lobbying expenditures) to that earned by selecting the NE. This sign changed compared to the previous equation, shows the “upper bound”.

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Regulated CPR Model – Non-Cooperative Lobbying So, we’ve now identified the ranges wherein non-cooperative lobbying could occur.

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Regulated CPR Model – Cooperative Lobbying Lobbying expenditures to increase a proposed regulation are as follows: Below is a comparison of the cooperative & nc boundaries. This now has group size in the denominator, which causes the boundaries to be smaller compared to the nc model.

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Regulated CPR Model – Cooperative Lobbying Lobbying expenditures to decrease a proposed regulation are as follows: As before, a boundary exists where a group would NOT want to lobby using these equations. A group would compare the group profit earned at their respective upper bound (minus the group’s lobbying expenditures) to that earned by selecting the NE. This provides an interesting case where cooperative behavior fails, mainly as a result of the cost of lobbying. This sign changed compared to the previous equation, shows the “upper bound”.

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Summary (1) In an unregulated setting, individuals have no incentive to deviate from the Nash equilibrium in our model, (tragedy of the commons). (2) In a regulated setting, individuals may be bound by the regulation and no longer able to extract from the resource according to the unregulated Nash equilibrium. (3) There is a range about a group’s social optimum where lobbying is no longer profitable, which gets smaller when groups act cooperatively.

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Concluding Remarks Regarding resource sustainability, we observe two positive outcomes with regards to lobbying: (1) Individuals may lobby for a stronger regulation on resource use. (2) If individuals act non-cooperatively, the region increases in which lobbying is no longer profitable; this may prove useful when individuals would prefer a weaker regulation.

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Questions? We gratefully acknowledge the support for this research provided by a NOAA/Sea Grant Joint Fellowship in Marine Resource Economics and by RI Sea Grant.

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