Tragedy of the Commons

An open-access fishery — each fisher maximizes their own catch, but the stock is shared and finite

Ecosystem Parameters
Carrying capacity (K)1000
Growth rate (r)0.30
Fishers (N)5
Price per fish (p)10
Cost per boat (w)50
Stock growth: S' = S + rS(1 − S/K) − H
Catch per boat: q·S/N_total_boats
(more boats & less stock → less per boat)
Profit = p·catch − w·boats
MSY = rK/4 at S = K/2
Policy Regime
Open Access
Tax
Quota
ITQs
Open access: No regulation. Each fisher sends as many boats as they want. Classic tragedy — entry continues until profit = 0, overshooting the MSY.
Tax per fish caught0
Pigouvian tax: Raises the effective cost of fishing, reducing effort to a sustainable level. Revenue goes to the regulator. Set tax to internalize the stock externality.
Total Allowable Catch200
Catch quota (TAC): Regulator sets a total catch limit, divided equally among fishers. Prevents overharvesting but may create a "race to fish" within the season.
Total quota200
Individual Transferable Quotas: Each fisher gets a tradeable share. Eliminates the race to fish and allows efficient allocation. Your share: — fish.
Bot Behavior
Season 1
Fish Stock
1000
0 (collapsed) MSY at 500 K = 1000
Your Profit
0
Your Catch
0
Total Harvest
0
Season
1
Your fishing effort (boats)
0 20
3
Cost: 150  |  Est. catch: —  |  Est. profit: —
🐟💀 The fishery has collapsed! Stock fell below recovery threshold.
Reset to try a different approach.
Each boat you send catches fish proportional to the stock and inversely proportional to total boats. More boats = less per boat. The stock regenerates each season via logistic growth — but only if enough fish remain.
Fish Stock Over Time
Stock Level
MSY Stock (K/2)
Collapse Threshold
Harvest & Sustainable Yield
Total Harvest
MSY (rK/4)
Natural Growth
Cumulative Profits
Your Cum. Profit
Avg Bot Cum. Profit
Optimal Sustainable Profit
Effort (Boats) Per Season
Your Boats
Total Boats
The Commons Problem Explained
The Externality
When you send a boat, you reduce the stock available to everyone else — but you don't bear that cost. Each fisher ignores the stock externality, leading to over-entry.
Open-Access Equilibrium
Entry continues until profit per boat = 0. This happens at a stock level well below MSY. Rents are fully dissipated — the fishery generates zero economic profit.
Maximum Sustainable Yield
MSY = rK/4 = — fish/season at stock S = K/2 = —. A sole owner would harvest at this level to maximize long-run value.
Policy Solutions
Tax (raise costs), Quota (limit total catch), ITQs (tradeable shares — most efficient). All aim to reduce effort to the level a sole owner would choose.