As a class, they have a set of similar incentives (grow/retain resources and power networks) that lead to similar actions (avoid taxation, buy influence, weaken regulators, etc). They may cooperate at times, but they are not a coherent organization with a roster, votes, and leadership.

As individuals, they are dangerous competitors, and they can’t afford to trust each other too much without some kind of mutual leverage. This could be in the form of mutual equity holdings, blackmail, complex arrangements where each party has exposure, whatever. But even then, trust has limits.

There’s no cabal that runs things with rules and elections at this level. It’s all individuals who are immersed in the systems that made them wealthy. Those systems tend to lead to certain behaviors. That’s it.

It doesn't need any intelligence at all. There's mutually beneficial things to any group of people. So it doesn't require explicit coordination. Even fairly unintelligent animals have symbiotic relationships with other species. So your argument is what, that billionaires are less intelligent than an ant?

Look into a class on systems thinking.