Each period, each student in a group decides how many hours to spend fishing from an open-access lake (a common-pool resource). At the end of each period, every player learns the total hours spent fishing, as well as the hourly return from fishing. The tragedy of the commons stems from the fact that revenue from each hour of fishing is decreasing in the overall level of total fishing, and the profit-maximizing player does not take into account that her fishing reduces the return for other players.
In this game, the fishery returns to full health after each period, so the societal cost of overfishing is borne in the current period: the overall level of fishing this period determines the returns from an hour fishing. For a game where over-exploitation of a common-pool resource this period reduces future ability to benefit from a common-pool resource, see our Tragedy of the Fish game.
Since fish in a public lake are a common resource, each individual has an incentive to overfish (i.e., not take into account the cost imposed on other group members).
Regulations, such as taxes or subsidies, can mitigate the over-use of natural resources.
With repetition, group play should converge to the neighborhood of the Nash equilibrium outcome, and thus over-fishing, absent a tax or subsidy. It will take approximately 3-4 periods for most groups to converge. Period Duration determines the length of each trading period. All periods must be completed within the time you allot in the Duration panel.
Each period, the most each player can fish is equal to Total Fishing Hours divided by Group Size. Per-hour revenue from fishing equals Total Fishing Hours minus the number of hours fished by group members.
In choosing how many hours to fish, a student has access to a Revenue Estimator. The estimator displays hourly revenue as the student varies both the number of hours she may choose to fish and the her prediction of the average hours chosen by group members.
With repetition, group fishing will generally exceed the efficient level and land near the Nash equilibrium level. To make the strategic interaction more salient, we recommend keeping Group Size relatively small (e.g., 5 or fewer).
In the one-shot Nash equilibrium, with N equal to Group Size each player chooses:
$${\small hours_{i}^{\text{Nash}}=\frac{\text{Total Fishing Hours}}{N + 1},}$$for a group total of
$${\small Hours^{\text{Nash}}=\frac{N}{N + 1}\text{Total Fishing Hours}.}$$In contrast, the efficient level of exploitation is
$${\small Hours^{\text{efficient}}=\frac{1}{2}\text{Total Fishing Hours}.}$$By default, Total Fishing Hours=120 and Group Size=5. In equilibrium, each player spends 20 hours fishing, whereas the efficient level has 60 hours in total (or averaging 12 hours each).
As students are restricted to integer choices, integer Nash quantities are desirable. Holding Total Fishing Hours fixed at 120, both the Nash level of fishing and an even split of the efficient level are integers for Group Size equal to 2, 3, 4, or 5 players.
One solution to Tragedy of the Commons is to tax fishing. To solve for the optimal tax, we solve the optimization problem with tax and choose the tax level that induces the efficient number of hours fished $${\small Hours^{\text{efficient}}=\frac{1}{2}\overline{\text{Hours}}.}$$ where Hours=Total Fishing Hours. $${\small \frac{\overline{\text{Hours}}-Tax^*}{N+1}=h_{i}=\frac{\overline{\text{Hours}}}{2 \times N}}$$ $${\small Tax^* = \frac{\overline{\text{Hours}} \times (N-1)}{2 \times N}}$$ Therefore, make sure Group Size is odd to ensure that the tax inducing the efficient level of fishing is an integer.
As an alternative to a tax on each hour fished, you can implement a subsidy for each hour not fished. As a dollar paid has the same effect as a dollar not received, the optimal subsidy equals the optimal tax calculated above.
The results we present allow you to see, each period, whether players converge towards Nash equilibrium play, and how this affects group profits.
The table (Figure 1) allows you to compare each group's outcome (average quantity and resulting average profit) to two benchmarks: the efficient outcome and the Nash equilibrium.
The Production Graph displays the market demand curve, and identifies each group's production along it. It also shows the monopolist's quantity (i.e., perfect collusion) and the Nash equilibrium total quantity.
Note that you can dynamically choose which elements to include in the graph. For example, to remove the monopoly and Nash benchmarks, uncheck the appropriate boxes in the legend.
With repetition, you should see groups move towards the Nash prediction. If you played a game with multiple rounds, you can click the button next to Go To: to show the Production Graph for different rounds. If you replayed a particular game, display the results of the last game. You can then look at previous games in the series by clicking the button next to View:.