Payoff table: Both swerve: both lose face Neither swerve: both die They swerve, you don't: you gain face, they lose it You swerve, they don't: you lose face, they gain it
So: you make it abundantly clear that you can't control your car, even if you wanted to. Tear out the steering wheel, or lash it down and jump onto the roof of the car. Now it changes your opponents options to:
Swerve: lose face Don't: die.
(It's a trolley-problem-like scenario, don't ask too many questions about the practicalities of tearing out the steering wheel)