What you're talking about is something like (if not exactly) game theory. I read somewhere (no source sorry) that humans in normals situations DON'T actually behave like that.
They generally come to a mutually satisfactory conclusion, normally kindness (apparently inherent in human society) surfaces quickly.
Intelligence would perhaps suggest it's most efficient not be a dick in the long run.
First: You don't get what you don't ask for. the other person might really only want a quarter of the cake, but by asking for more than your "fair share" you open the door to allowing them to give you what you want.
Second: By asking for the whole thing, you have placed yourself in a position of power and privilege. The mere act of asking for more implies that you think you deserve it. Someone mentioned posturing in another comment.
Learn to spot and understand the perspective of people who expect to get the whole cake in life - the loser/clueless/sociopath model being of some use here:
I work in customer service for a sub-unit of a large telco. When people run into annying issues, I am kind of at liberty to issue a refund if I want to, sort of to please the customer and make them stay with us.
However most people don't ask for it. So only the ones who take the time to ask for it and write two sentences of why they should receive one get it.
The reasonable person asks for half the cake, the unreasonable person asks for the whole cake.
They compromise and split the difference - the unreasonable person gets three quarters of the cake and the reasonable person gets a quarter.
[I wish I knew the origins of this - I heard it years ago.]