This is an interesting puzzle! and interestingly, I didn't know there's people who do research and write papers on game theory

I bet that job is so much fun, playing game everyday!
That paper does look complicated, i just had a quick look and gave up reading and understanding it... and just sat down, lay out the coins in front of me and think and try it out.
It took a while, and when i figured out how to do it, i wanna bang my head with a pot

, as the paper said, you really can move the 10 coin pyramid upside down with just 3 moves! very simple.
Here the reference:
Pyramid size->Minimum moves required to make pyramid upside-down
3 coins -> 1 moves
6 coins -> 2 moves
10 coins -> 3 moves
15 coins -> 5 moves
21 coins -> 8 moves
Hint: clockwise or counter-clockwise, stick with one
