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Commons: Fishery with Quota

Game Description

Each round, each student decides how many fish to catch from an open-access lake (a common-pool resource). The tragedy of the commons occurs when overfishing prevents the sustainability of the fish stock for future use. Either before or after players have depleted the fish stock, the instructor can implement a quota to manage the fish stock, resulting (eventually) in higher per-round payoffs.

MobLab offers three different games covering the Tragedy of the Commons, each highlighting different aspects. The following table (with the current game listed first) shows how these games differ.

Commons: Fishery
with Quota
Commons: Fishery Tragedy of the
Commons
Target Class Upper Level Intro Upper Level
Resource Recovery
Between Rounds?
Partial Partial Full
Exploitation Costs Incurred Future Rounds Future Rounds Current Round
Available Policies Quota None Tax Use/
Subsidize Restraint

We thus have two different types of common-pool resources. In the first two games, the level of exploitation in the current round determines the size of the resource in following rounds. In the last game, the resource is fully replenished each round, but the returns to an individual’s current-round use depends on the sum of everyone’s current use.

Learning Objective 1: Tragedy of the Commons

Since fish in an open-access fishery are a common resource, each individual has an incentive to overfish.

Learning Objective 2: Resolving the Tragedy of the Commons

A quota can improve player outcomes relative to open access, both by allowing the recovery of a renewable resource and by preventing over-exploitation of a healthy stock.

Brief Instructions

Each round t, each player i simultaneously chooses an effort level (ei,t) between 0 and 100. A player’s catch equals $$\mathrm{Catch}_{i,t}(e_{i,t})=s_t \times k_i \times \frac{e_{i,t}}{100},$$ where ki is her fleet’s capacity and st is beginning-of-round fishery stock as a fraction of maximal stock. (The fishery’s maximal stock (\(\overline{S}\)) equals 300,000 × Group Size.) She receives $5 per fish caught, and incurs costs $$\mathrm{Cost}_{i,t}(e_{i,t})=F_i+80e_{i,t}^2-50e_{i,t}.$$

Within each group, players are evenly divided amongst three fleet sizes: {\(k\!=\!250,000,F\!=\!$50,000\)}; {\(k\!=\!300,000,F\!=\!$70,000\)}; and {\(k\!=\!350,000,F\!=\!$90,000\)}.

The sum of player catches determines each round’s stock depletion. Between-round stock growth is determined by the reproduction fucntion, $$S_t=\sigma_{t-1}\left((1+g)-\frac{g\times\sigma_{t-1}}{\overline{S}}\right),$$ where \(S_t\) is the beginning of round fish stock, \(\sigma_{t-1}\) is the ending fish stock in the previous round, and \(\overline{S}\) is the fishery's maximal fish stock. You set the Growth Rate (%) (g). With Growth Rate (%) between 30 and 50, the fish stock will functionally crash after approximately 3 Open Access Rounds.

After the specified number of Open Access Rounds, students play a number of Quota Rounds. In quota rounds, each round’s catch is limited to a per-round Total Allowable Catch (TAC). The number of quota units each round is equal to 20 times Group Size. Each player’s Allowable Catch is equal to that round’s TAC her quota units as a fraction of all quota units. It then takes at least 3–5 Quota Rounds to restore the fishery to its target (i.e., healthy) stock. Players can expect relatively low profits during these initial stock-rebuilding rounds.

Key Treatment Variations

Quota Allocation

By default, Quota Allocation=Equal, meaning each player has the same number of permits, and thus the same allowable catch. Setting to History allocates permits in proportion to each player’s catch in the final open-access round, and setting to Capacity allocates permits in proportion to each player’s capacity. Compared to the default of an equal allocation, both of these alternatives will both advantage larger fleets (i.e., those with a larger capacity) and increase group profits.

Note that you can only use History if the game has at least one open-access round. Also, If players know that quota allocation is proportional to their catch in the final open-access round, many players will choose effort levels (and thus catches) in excess of short-run profit maximization in this pre-quota round.

Stock Recovery Rule

By default, Stock Recovery is set to Half of Growth. If stock at the end of round \(t\!-\!1\) is less than one-half maximal stock, then allowable catch in round \(t\) is one-half of the growth between rounds \(t\!-\!1\) and \(t\). If end-of-round stock is greater than one-half maximal stock, then allowable catch in round \(t\) is twice the inter-round growth. One downside of this rule is that when stocks return to the neighborhood of one-half maximal stock, TAC, and thus profits, may vary widely from round-to-round.

Alternatively, set Stock Recovery to to Increasing Fraction of Growth. You will also need to set Number of Recovery Rounds (\(\tau^*\)), which determines the number of rounds needed to return the stock to one-half the maximal stock. In particular, with \(\tau=1\) equal to the first quota round, $$TAC_\tau=\max \{0,G_\tau-\frac{S^*-\sigma_{\tau-1}}{\max \{\tau^*-\tau,1 \}} \}.$$

Important: A small number of recovery periods relative to the stock’s growth rate will require a temporary closing of the fishery. In the following examples, we assume a crashed fish stock (i.e., after 4 open-access rounds).

Growth Rate = 30: To restore the stock in 5 rounds, the fishery must be closed for 5 rounds. In order to have no rounds in which the fishery is closed, set Number of Recovery Rounds to 8.

Growth Rate = 50: Setting Number of Recovery Rounds to 5 results in a smooth transition to the target stock. Trying to return to target stock in 3 or fewer periods requires a temporary closing of the fishery.

Initial Stock (%)

Because growth is maximized when end-of-round stock is 50% of maximal stock, the default Initial Stock (%)=60 starts the game with a healthy fishery.

To compare recovery regimes, you may want to start with a crashed stock and have students only play quota rounds (i.e., set Open Access Rounds to zero.) With growth rate equal to 50%, use an initial stock of 30 percent, and with growth rate equal to 30%, use an initial stock of 22%.

Results

Figure 1: Average Beginning of Round Stock

We first present a graph illustrating the average state of the fish stock at the beginning of each round (Figure 1). By default, Open Access Rounds and Quota Rounds are each set to 5. With these conditions you will see the fish stock deplete through round 5, and then recover once the quota is introduced.

Figure 2: Average Profit Per-Round

Next, a graph showing the average profit per-round is shown, delineated by each of the three fleet sizes (Figure 2). To hide a fleet's results, click the checkbox next to the desired fleet in the legend.

If multiple games were run, use the View drop down menu to switch between games or choose the aggregate results option. In the aggregate results screen, the Average Beginning of Round Stock graph will show different colored bars for each game played. Instead of showing a single graph for Average Profit Per-Round, there will now be three separate graphs showing each game's average profit by fleet size.

If the game is replayed with different parameters, click the results button on the last game run. To compare results between these games, choose the Compare option in the top right of the results screen. This allows you to show results from two different games simultaneously.

Robot Play

Our robot (i.e., an automated player) strategies are the following:

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