At the beginning of the game, your character's personality is determined by how he/she acts in a situation set before him/her in a dream, such as burning or sparing the citizens of a town when transformed into a monster, jumping off a tower or not, or deciding whether to attempt to save a man dying in the desert or abandoning him to die.
Can the same thing be done in a story where a character is placed in a situation and he/she reacts as such?
If the player is controlling the character at this point in the game, the personality that is determined is not the character's, but is, instead, the player's.
Does the act define the character, or does the character define the act? For example, consider that there are two people who intentionally crashed a car into a tree and survived.
What is important is not the act itself, but the reasons for the act, the character's reaction to the act, and the emotional growth or collapse due to the act. The first person in the above example could be angry because he or she flunked a course, got expelled from college, decided to cope with the shame by attempting suicide, and failed in this attempt due to the air bag deploying. The second person could be just as angry because he or she realized, after crashing the car to relieve stress from a domestic dispute, that the car insurance purchased was not full coverage.
Characters can do almost anything, but their actions need justification.
Have you ever had a dream like this in real life?
Well . . . if I ever do, I assume that I would act like I normally do because usually in my dreams I can not tell whether or not they are indeed dreams at the time of occurrence. And when I do eventually find out that I am in a dream, I usually become half-awake or completely awake, so what I would continue to do would become speculation and not actual action because I could then do almost anything without fear of consequence if i knew that I was in a dream--suggesting that what I later did would have no eventful meaning.
Though experimenting in your dreams can sometimes be fun, as you can act outside the norm.