Combat is the most common example. This is handled simply by having both contestants roll dice. If both succeed or fail the situation is unlikely to change much. Otherwise the GM tells what has happened. If the result is unsatisfactory to the PC, he can use a Fame roll to change things.
Modifiers have a special meaning in opposed tasks.
Most nerds would not even try to resist. This generally works in combat as well. All combat follows the next five steps. All persons in a film act in the order of their Fame attributes, with higher numbers going first. Someone with high initiative can wait and let others go first.