Game theory is not the best way to think about the tragedy of the commons.

Elinor Ostrom got in 2009 the "nobel prize" in economics for her work of studying how people actually deal in the real world with the tragedy of the commons. It makes much more sense to go to her empirically derived work than to think in terms of game theory.

She suggests 8 principles:

1. Clearly defined boundaries (effective exclusion of external un-entitled parties);
2. Rules regarding the appropriation and provision of common resources that are adapted to local conditions;
3. Collective-choice arrangements that allow most resource appropriators to participate in the decision-making process;
4. Effective monitoring by monitors who are part of or accountable to the appropriators;
5. A scale of graduated sanctions for resource appropriators who violate community rules;
6. Mechanisms of conflict resolution that are cheap and of easy access;
7. Self-determination of the community recognized by higher-level authorities; and
8. In the case of larger common-pool resources, organization in the form of multiple layers of nested enterprises, with small local CPRs at the base level.