Tragedy of the Commons: Resource Depletion Simulation

simulator intermediate ~8 min
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Collapse at generation ~45 — the commons is overexploited

With 10 agents, 15% harvest rate, and only 20% cooperation, the shared resource collapses within roughly 45 generations. Increasing cooperation to 60%+ typically prevents collapse, demonstrating that the tragedy is not inevitable.

Formula

R(t+1) = R(t) + r·R(t)·(1 - R(t)/K) - N·harvest_rate·R(t)
Maximum Sustainable Yield: MSY = rK/4
Sustainable population level: R* = K/2

The Tragedy of the Commons

In 1968, ecologist Garrett Hardin published one of the most influential papers in environmental science. He described a shared pasture where each herder has an incentive to add one more animal — the herder gains the full benefit of the extra animal but shares the cost of overgrazing with everyone. If all herders follow this logic, the pasture is destroyed. This is the Tragedy of the Commons: individual rationality leading to collective ruin.

The Resource Model

This simulation uses logistic growth: the resource regenerates following R(t+1) = R(t) + r·R(t)·(1 - R(t)/K) - harvest. The growth rate is fastest at K/2, creating a natural 'sweet spot' for sustainable harvest. The Maximum Sustainable Yield (MSY = rK/4) represents the largest possible extraction rate that the resource can sustain indefinitely.

Cooperators vs. Defectors

The simulation divides agents into two types. Cooperators (cyan dots) limit their harvest to the sustainable rate — they share the burden of conservation. Defectors (red dots) extract at the full harvest rate, maximizing their short-term gain. The key parameter is the cooperation percentage: how many agents restrain themselves.

The Critical Threshold

Slide the cooperation percentage and watch the resource curve. Below a critical threshold, the resource collapses — defectors extract faster than the resource can regrow. Above the threshold, the resource stabilizes near K/2. This threshold depends on the harvest rate, regrowth rate, and number of agents. Finding and maintaining this threshold is the central challenge of commons governance.

Beyond Hardin: Ostrom's Solution

Hardin argued that only privatization or government control could prevent the tragedy. But Elinor Ostrom demonstrated through decades of fieldwork that communities around the world — fishermen, irrigators, forest users — successfully self-govern commons through institutions based on clear rules, monitoring, graduated sanctions, and conflict resolution. Her work, which earned the 2009 Nobel Prize in Economics, showed that the tragedy is not inevitable when communities can communicate, build trust, and establish norms of reciprocity.

FAQ

What is the Tragedy of the Commons?

The Tragedy of the Commons is a situation in which individual users, acting independently according to their own self-interest, deplete a shared resource, even when it is clear that this is not in anyone's long-term interest. The concept was popularized by ecologist Garrett Hardin in his 1968 Science paper.

What is the logistic growth model used here?

The resource follows logistic growth: R(t+1) = R(t) + r·R(t)·(1 - R(t)/K) - harvest, where r is the intrinsic growth rate and K is the carrying capacity. This creates an S-shaped growth curve that slows as the resource approaches K.

What is Maximum Sustainable Yield?

Maximum Sustainable Yield (MSY) is the largest harvest that can be taken from a renewable resource indefinitely. For logistic growth, MSY = rK/4, achieved when the population is at K/2. Harvesting above MSY leads to eventual depletion.

How did Elinor Ostrom solve the tragedy?

Elinor Ostrom, who won the 2009 Nobel Prize in Economics, showed that communities around the world successfully manage shared resources through self-governance, without privatization or government regulation. She identified 8 design principles for successful commons management, including clearly defined boundaries, collective decision-making, and graduated sanctions.

Sources

Embed

<iframe src="https://homo-deus.com/lab/game-theory/tragedy-of-commons/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub