The honest answer is nobody knows exactly what that looks like at scale. Markets with millions of automated agents optimizing simultaneously could behave very differently. That's pretty wild to think about.
But I think the more immediate reality is much more mundane. Right now these assistants are reading your email and reminding you about dentist appointments. We're a long way from autonomous agents negotiating on your behalf at scale. The infrastructure isn't there, the trust isn't there, and the coordination protocols between agents don't really exist yet. When we do get there, it probably looks less like a free-for-all and more like new norms and rate limits emerging, the same way APIs and marketplaces already throttle automated access. That's my guess.
The interesting question to me is who builds those protocols and whether they're open or proprietary.