I read this interesting experiment from The Origin of Wealth, a book by Eric B. Beinhocker (paraphrased):
Imagine that a stranger proposes you and me the following deal. She will give us 5,000$ if we can agree on how to split it. It works like this: I choose a split and you don't get to negotiate it, you can only accept the deal (in which case each of us gets what I chose) or reject it (in which case neither of us gets anything).
After giving it a short thought, I propose that I get 4,990$ and you get 10$.
Would you accept the deal?
(I'm not asking what you think is the rational thing to do from either a selfish or political standpoint, but what would you actually do.)
Well it would depend on how well I knew you. It didn't say if you and I are strangers. If I knew you needed an operation that cost $4,990 and we were friends then this deal would be considered a windfall and I'd agree to it.
If you and I are strangers, then considering we know nothing about each other, I would say no because all else being equal, why should we get unequal amounts?
This reminded me of an article on why psychopathy still exists in the world and how to reduce it. Basically it comes down to it making sense in game theory unless mitigated by reputation. Psychopaths get away with stuff by papering their reputation and smearing others'. If people don't reduce the psychopath's reputation, they will get away with anything.
In this case I wouldn't want to give myself the reputation of accepting less than half with strangers, in case I needed more in the future, unless I was very secure knowing that I wouldn't ever need more. Also I wouldn't want to give the stranger the sense that they can take more than half with strangers, because maybe my friend or family member in need will be in the same transaction in the future? If this person has a bad reputation then absolutely we will neither get any money. If this person has a great reputation then I would assume they possibly made a more well-informed decision, an error or were joking, and we could come to a mutually satisfying understanding after the deal. (See why it's important to reduce a psychopath's reputation? If they don't have a reduced reputation they will get away with anything. Also they smear others' reputations to leave less for others and more for themselves.) If we're strangers maybe this person is a psychopath or has a bad reputation that I don't know about and I wouldn't want to reward them. Beside all this it's basically a chance for each to gather information of the part and whole.