Unfortunately, non-zero sum games do not have good solutions, particularly if there are non-rational players.

The classic example is the game of Chicken, where two people drive cars at high speed toward each other, and the first person to balk loses.

As I'm sure you know from game theory, the "best" solution if you don't want to lose is to take your steering wheel off and throw it out the window so your opponent sees that you cannot swerve.

Of course, if both players do this, they both the game, and lose their lives.