Experiment 08 Shared Resources
The Last Fish
Share a replenishing lake with three other boats. Test whether the rules leave enough fish for next season.
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Start with “Work It Out, Step by Step” below. The optional expert section explains its symbols as you go. For more examples, use the plain-language math guide.
1. Make a Prediction
Four Boats, One Lake
Your boat and three others share a lake that starts with 80 fish. After each season’s catch, the remaining fish reproduce. A common resource is something people share that can be used up: a fish caught by one boat is no longer available to the others. Unlike the public-goods game, the problem here is how much to take, not how much to contribute.
2. Make Your Choice
Fish in the lake: 80 of 100.
3. Reveal the Incentives
Catch Today and Fish Tomorrow
Each fish caught earns one point. Monitoring costs each boat up to one point per season. A large catch can improve your earnings now and leave fewer fish to reproduce. The history shows whether the whole lake is recovering or being depleted, meaning used up.
| Season | Your catch | All boats’ catch | New fish | Next season’s stock |
|---|
4. Change One Assumption
Can the Boats Make a Rule That Lasts?
A quota is an agreed limit on how much each boat can take. Monitoring means checking whether boats follow the rule. Here it prevents the chosen percentage of any request above the quota. For example, 50% monitoring prevents half of the excess. Each boat pays the monitoring percentage divided by 100 in points, even if its own request follows the rule.
With the local agreement on, the three other boats voluntarily lower requests to the quota. You still choose your request and can break the agreement, subject to monitoring. This is a fixed cooperation rule, not a negotiation simulation.
Model assumptions: all boats fish at the same time. If requests exceed the available fish, each receives the same fraction of its allowed request. Fractional fish represent average catches across many small fishing areas. Growth uses only fish left after the catch, stops at a capacity of 100, and is zero when no fish remain. Real ecosystems have more complex growth and uncertainty. Changing a rule starts a fresh lake.
Work It Out, Step by Step
Use the starting rules: 80 fish, four boats each catching 6, 50% growth, and no monitoring.
- The boats catch \(4 \times 6 = 24\) fish altogether. The multiplication sign means four groups of six.
- Subtract the catch: \(80-24=56\) fish remain.
- Fifty percent means half. Half of 56 is 28 new fish.
- Add the new fish to the survivors: \(56+28=84\). The lake ends larger than it started.
- If each boat catches 20 instead, all 80 fish are removed. Half of zero is zero. There are no parents left to produce new fish.
In words: take away this season’s catch, then multiply the remaining fish by 1.5 to include both the original fish and their 50% growth. Stock means the number of fish currently in the lake. Capacity means the largest stock this simplified lake can hold.
For experts: formal model and assumptions
How to Read the Symbols
- \(S\), \(H\), \(g\), and \(K\)
- \(S\) is the starting stock this season; \(H\) is total actual harvest; \(g\) is growth written as a decimal, such as 0.5 for 50%; \(K=100\) is capacity. A letter is a short name for one amount.
- \(S_{\text{next}}\) and \(\min\)
- The small word “next” labels next season’s stock. \(\min(a,b)\), read “the minimum of a and b,” means choose the smaller of the two amounts. A comma separates the choices, not a decimal.
In words: grow the surviving stock, but cap the result at 100. Harvest cannot exceed stock. When demand exceeds stock, multiply every allowed request by stock divided by total allowed requests. That gives all boats the same percentage of their request.
The enforcement rule removes a fixed fraction of each request above the quota; the app does not randomly inspect individual boats. Group earnings equal total harvest minus monitoring costs. Future fish are shown separately instead of being assigned a made-up money value. There is no claim that a chosen quota is optimal for a real fishery.
See the math reading guide for percentages, multiplication, and small labels.
5. Transfer the Lesson
Sharing a Limited Resource
A neighborhood draws water from the same underground supply. What would you need to know before setting a quota? How could residents help choose and monitor rules, and what would happen if the supply replenished much more slowly than expected?
Concept reference: Elinor Ostrom’s Nobel lecture on governing shared resources. Local rules and monitoring can matter; this small lake is not a test of every possible institution.
A Model Is a Place to Start
These small models make the incentives visible. Their results follow from their stated rules; they are not forecasts of how every person or organization behaves. A simulated strategy is a rule, not a personality.
Scenario links save the controls and random seed. To reproduce an interactive run, make the same choices in the same order. Changing a setting restarts the experiment.