I have to agree with some of the commenters that your write-up is pretty bad, because far too general for such a well studied problem. Let me try to help you a

I have to agree with some of the commenters that your write-up is pretty bad, because far too general for such a well studied problem. Let me try to help you along in your thinking: The tragedy of the commons is not a generalized version of the prisoner dilemma. I guess you meant to say a prisoners dilemma is a more generalized version of the tragedy of the commons. This is however also not true. Logically because there is no sensible pay-off where everybody defects, but the other player. The commons would be largely destroyed way before everyone gets their pay-off so all the players would never collectively decide to do that (and decision is a integral part of the prisoners dilemma). You could make it into a NxN dimensional prisoners dilemma, but that is not useful for another reason. The tragedy of the commons is about future benefit (keeping the commons so everyone can extract more than they could individually at a single instance) a prisoners dilemma is an instant game. You could model the tragedy of the commons as a repeated prisoner dilemma. The problem is that free riding is not a rational option if you repeat it often enough. In the real world free-riding works, because we expect to play a limited number of rounds and in the long term we are all dead. The number of repetitions one expects to play is however not the same for all players. Limiting defection is in this case not external to the tragedy of the commons, as any way to resolve the prisoners dilemma is, because it reduces the pay-offs the participants get. Preventing defection costs and there is a balance to be struck to the costs to preventing an additional free-rider and letting him free-ride. There is also a moral component to this. Limiting defection means also being able to limit entry. The commons has de-facto become 'our commons'. There is the description of a 'mutual protective agency and one of the most common is the state.