This is an excerpt of Caplan and Stringham’s Networks, Law, and the Paradox of Cooperation.
I do not know enough about economics to comprehend any of that. I humbly request enlightenment.
Why do you think that’s ‘economics’ ? And do you think that because these people are usually regarded as ‘academic economists’ they are really making sense ?
This is not saying (or even trying to say) anything deeper than that a system of poly centric order is not the same as a monolithic order.
that multiple contracts between multiple parties is not the same as a single contract with all the parties as signatories.
Perhaps it doesn’t concern economics; I simply do not know enough about this subject to know its specifics. I still ask for help to decipher it.
I could be wrong, but i interpret the ‘anti collusion (N-2) part of the text’, as saying that, any other non-colluding agency (N-2) could derive profit from advertising the collusion and lack of justice provided by the 2 colluding agencies in question.
As if there were no top to the “pyramid”?
the law and order pyramid?
well, i think the providers of law and order services are the roof, its just organic rather than concrete [:P]
I think you got confused cus of all the fancy math stuff 
N(N-1)/2 is the total number of contracts possible between pairs of firms. N firms can make unique contract with every other firm except themselves (N-1), and in order not to double count you have to divide by Y! where Y is the number of firms in a contract so you divide by 2! = 2. I.e. A contract between A and B is the same as one between B and A.
And the (N-2) firm is "every other firm that is not involved in cette contract).