Here's some math showing that this pyramid is unstable. I'm assuming that you are taking a third of every level (as that would be the remainder).
Person 1 sends .1. One person is out .1, for a total defecit of .1. Owner has collected 0 total.
Person 1a sends .1, person 1b sends .1, person 1c sends .1. Person 1 collects .2, owner collectes .1. Three people are out .1, for a total defecit of .3. Owner has collected .1 total.
Person 1aa sends .1, person 1ab sends .1, person 1ac sends .1, person 1ba sends .1, person 1bb sends .1, person 1bc sends .1, person 1ca sends .1, person 1cb sends .1, person 1cc sends .1. Person 1a, 1b, and 1c all collect .2. Owner collects .3. Nine people are out .1, for a total defecit of .9. Owner has collected .4 total.
So now the nine people (1aa, 1ab, 1ac, 1ba, 1bb, 1bc, 1ca, 1cb, 1cc) all have to each get three people under them. As we can see from the pattern forming, .2 goes to the person above them and .1 to the owner. After this level, there will be 27 people out a total of 2.7, with the owner having collected a total of 1.3.
On the next level, those 27 people all have to get three people under them. The total defecit after this level will be 8.1, with the owner having collected a total of 4.
As you can see, for the pyramid to progress, you need exponentially more and more people to join. The total deficit rises and rises as you'll continuously have more and more people out money. When they get paid back, you have even MORE people out money. It's unstable because there aren't an infinite amount of people with an infinite amount of money...eventually nobody else wants to contribute, and the system stops, and the nature of something like this is that when it stops, it'll always be at the maximum deficit.
It will never stop. There will always be people investing, more people investing, people re-investing. It is a cycle. People would have to be stupid to surpass an opportunity to double this money.