Solving the tragedy of the commons. I wish you luck.
Interestingly, you hint at, but don’t really acknowledge one of the classic solutions (typically pushed by the libertarians): privatize the commons. This is equivalent to your intuition of trying to set N=1.
Of course, the other classic solution is regulation, which is not too far from your union example.
Of course, both the classic solutions have downsides. Privatization makes it harder for everyone to share the good, and also leads over time to stratification and unequal society. Regulation means bureaucracy, which easily becomes captive to politics and money.
There are a wealth of real world examples of communities working together to collectively manage the commons without either privatisation or state regulation.
If you want to know more you should familiarise yourself with the work of Elinor Ostrom.
There is a subtle technical difference in the literature, where regulation is externally imposed and codified, while communal management is devised, enforced, and most importantly, flexibly changed by those actually involved with the appropriation and management of the resource.
There are known “solutions” to the prisoners dilemma, which is the broader problem. (I say that in quotes because it always involves changing the problem in some way like adding a mafia Don or playing multiple rounds).
It seems to me that the problem with the Libertarian approach is finding a just way to actually privatize the commons. Since they are by definition common property, the rich have no greater claim on them than the poor. In future generations it wouldn't be just that some people had access to the former commons and some people don't due to the actions of their ancestors.
The only solution that I can see would be for those who own the commons to pay the profit that they gain from that ownership to those who do not own the commons. Which I guess is effectively Georgism.
so the non-libertarian answer to privatization of the commons is the pigovian tax. It's got most of the advantages (it uses the power of the market to maximize results per unit effort) and avoids some of the disadvantages inherent to privatizing things like air.
Take, for example, the problem of limiting CO2 output. This is a global problem; there is no way to realistically privatize it. but, at least the people under the same treaty could tax the common forms of CO2 output.
Charging per ton of CO2 output, many economists believe, is better than simply regulating how much CO2 a person can output because by giving it a dollar per tonne value, you are encouraging the market to eliminate CO2 output where it's cheapest and easiest to do so, while allowing the market to continue to output CO2 where it would be really expensive to avoid.
'cap and trade' is a variation on this that is similar but different; instead of setting the economic price of a tonne of carbon, for example, you set an absolute limit for how much carbon can be released, and then lets the market decide what to use that for.
That's exactly why we need a CO2 tax now and why the current "right" (who have largely been captured by the fossil-fuel industries) are fighting it tooth and nail.
Interestingly, you hint at, but don’t really acknowledge one of the classic solutions (typically pushed by the libertarians): privatize the commons. This is equivalent to your intuition of trying to set N=1.
Of course, the other classic solution is regulation, which is not too far from your union example.
Of course, both the classic solutions have downsides. Privatization makes it harder for everyone to share the good, and also leads over time to stratification and unequal society. Regulation means bureaucracy, which easily becomes captive to politics and money.