The Effects of Collective Defeat on the Nash Equilibrium

If agents have inaccurate credences about what each other will do then you can have some kind of collective defeat type thing going on. So for example suppose you and I both want to meet for lunch but we can't communicate. There are two possible places we could go to lunch the curry place and the pizza place. As bad luck would happen. You go to the pizza place and I go to the curry place so we fail to meet. But intuitively in this case the culprit is our false beliefs about what the other person would do. The culprit isn't the preferences themselves. If there are multiple Nash equilibria and again the agents can't communicate then it could turn out that they coordinate