Tragedy of the Commons

Overuse of a shared resource when individual users ignore the externality they impose on others.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

Each of $n$ users chooses effort $e_i$ ; resource yield is $f(E)=\sum_i e_i g(E)$ for aggregate $E=\sum_j e_j$ with diminishing productivity.

Nash equilibrium yields $E^{NE}>E^*$ ; the social optimum demands $f'(E^*)=\text{marginal cost}$ accounting for externalities.

Intuition

Each user considers only their own gain, ignoring the cost imposed on others through depletion.

Privately rational behavior aggregates into collective ruin.

Worked example

Overfishing in international waters and groundwater depletion are classic examples.

Traffic congestion is a commons-like equilibrium with excessive driving.

The math

Equivalent to a public-bad game; Pigouvian taxation internalizes the externality to implement the social optimum.

Ostrom (1990) documented real-world governance institutions that sustain cooperation without privatization.

Where it is used

Global fisheries exemplify the tragedy of the commons: each fishing nation maximizes its own catch, but the aggregate harvest depletes fish stocks below sustainable levels. The UN Law of the Sea and catch-share systems attempt to internalize this externality.

Groundwater extraction by farmers illustrates the commons dilemma: each farmer drills deeper to secure water, but collective overpumping lowers the water table for all. California's Sustainable Groundwater Management Act mandates coordinated usage plans.

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