The rich don't need the government to exert influence and rig the game in their favor. For example, they can: - buy up their competitors to create monopolies - use one monopoly to build another one (e.g. "if you buy our competitor's coal, you can't use our railroad") - gain control over natural resources - collude with their competitors - abuse the legal system to kill competitors - hire marketers and fund NGOs for propaganda purposes - control the media etc.

Once they have gained control over an industry, let's say steelworking or railroads, they become like feudal lords in that industry, setting wages and prices however they wish.

Power is subject to a positive feedback loop, whether it's political power or economic power. Having power makes it easier to gain more power. That's why it will always tend to concentrate in the hands of the few.

Government power in a democracy comes from a game of "artificial equality": elections in which every person has one vote, regardless of their power "in real life". (This is different from the economy, where your power is proportional to your wealth.) For this reason, it can act against the natural tendency towards concentration of power.