Once automated cars make up a significant fraction of cars on the road I would expect some communication scheme to emerge to make them coordinate with each other, maybe even sharing observed positions of other road participants.
There is the risk that they will misbehave or deadlock around each other, but also a great opportunity for them to communicate intent to each other at a level human drivers just can't do from a sound-insulated cabin.
My point is that it will take a lot of work to train them to communicate with each other. They are not smart enough to have a scheme simply pasted in, nor are human programmers adept enough to hard-wire a carefully-trained AI to have this scheme implemented. Absent extensive retraining you'd probably just have Waymos getting confused about all sorts of edge cases in the communication scheme itself.
I am not saying that it's doomed to fail - simulations can probably do most of the heavy lifting, and of course the tech itself will advance. I am saying it's a mistake to assume stuff like this is somehow a free lunch, or even "the easy part." It's unknowns about unknowns.
I would be surprised is they don't already share at the detailed map level. Was any published on how much the cars contribute to improving the map day after day (including temporary road closures and road work)? - but probably not yet directly when at the same intersection.
There is the risk that they will misbehave or deadlock around each other, but also a great opportunity for them to communicate intent to each other at a level human drivers just can't do from a sound-insulated cabin.