Chicken is not a good example of a random game. The best strategy is to be a bloody minded SOB, if you can’t convince your opponent that you are actually crazy. This is more or less what I got from Schelling’s essays in “Strategy of Conflict”.
And if you both do that, you both crash and die. It is not the best response to itself, so can’t be seen to be a Nash equilibrium.
Will_Pearson comments on Lawful Uncertainty