I think the matter is well documented. Wealth is not a zero-sum game. However--you have countries that deliberately hold people down. Everyone wants safety nets and such. That all has a huge effect on individual upward mobility.
Wealth might not be a zeronsum game, but we need to prevent someone to play it as such.
Imagine an economy where wealth is accumulated more and more to a few, then even the total wealth grows, how everyone enjoy them equally? If not equally, the inequality soon will make wealth zero sum anyway.
