wait, what? how does UDT make this calculation right for Alice? Bob is wrong (from all of her knowledge and all paths for her to update). Her utility is a direct mapping of the outcome of the bet—what path of communication does Bob’s expected value take to get to her?
For a non-altruist, this is clearly a chance for Alice to money-pump Bob. But the setup of the problem is that Alice gets utility from Bob’s actual money outcome, not his beliefs. Once Alice is done updating (leaving her at 2⁄3 chance of heads), that’s her belief, and it doesn’t change after that.
Her utility is a direct mapping of the outcome of the bet—what path of communication does Bob’s expected value take to get to her?
I am not quite sure what you mean about this, but I had Alice and Bob discuss at the begining so that Alice would know Bob’s probability, and I was assuming utility of the dollar was positive. That is all she needs to know Bob’s (normalized) expected value.
wait, what? how does UDT make this calculation right for Alice? Bob is wrong (from all of her knowledge and all paths for her to update). Her utility is a direct mapping of the outcome of the bet—what path of communication does Bob’s expected value take to get to her?
For a non-altruist, this is clearly a chance for Alice to money-pump Bob. But the setup of the problem is that Alice gets utility from Bob’s actual money outcome, not his beliefs. Once Alice is done updating (leaving her at 2⁄3 chance of heads), that’s her belief, and it doesn’t change after that.
I am not quite sure what you mean about this, but I had Alice and Bob discuss at the begining so that Alice would know Bob’s probability, and I was assuming utility of the dollar was positive. That is all she needs to know Bob’s (normalized) expected value.