What are the determinants of operating (running) an optimal pyramid scheme ?
A pyramid scheme relies on the building of a base of investors - the base of the pyramid, if you will. Only by having new investors handing over money will you have a continuation of the scheme. As soon as new recruits stop entering, people stop making money. So the first determinant of running the scheme is to guarantee to new recruits.
Thus, the next determinant is based on how to recruit. Legal "multi-level marketing" schemes are the best pyramids for getting new recruits because they require the selling of a product. Thus, there is a tangible money maker that the potential recruits can see and can have to sell, which guarantees income. However, in a true pyramid scheme, the determining factor is to have a base of potential recruits that each new recruit can then turn to in order to start their part of the scheme. Without that base in place - without the reassurance that they will be able to bring in new recruits after them - there will little success in getting anyone to join the pyramid.
Another determining factor is how to market the initial investment. Saying to someone, "give me a $100, and then go get $100 from 10 other people," is not likely to encourage participation. Therefore, the scheme operator must have the language and investment "plan" in place, and may consider using terms like "loans" and "gift giving" to make the initial investment seem more palatable.