Yes, it IS a game of chicken.
In the part of town where I live, idiots often cross wherever and whenever they feel like, with no interest in what the rules might be. When they start to do that in front of me and I have the right of way, I look right at them and keep the power on. (In reality, I'm not going so fast I CAN'T stop, but let's not give that impression.) Mostly they stay where they belong out of a desire to not become roadkill. But even then you get kids that look back at you and act like they're going to jump out in front of you, just to see if they can scare you into swerving or locking brakes up. They find that amusing. And THAT'S when they know there's a really good chance of them being DOA if they did it for real. What happens when they KNOW the car will slam stop to avoid them?
The poster above who mentioned "stand and deliver" is exactly right. If we wind up with automated cars that stop at the slightest provocation by a pedestrian, we'll either have to have police round these idiot pedestrians up and penalize them severely enough to make them stop (zero chance of that around here), not use automated cars or learn to enjoy having cars slam on the brakes suddenly for yet another idiot, sitting in traffic jams and being robbed while sitting there.
Or maybe add a manual override -- and then we're back to where we are now.