I believe I’ve found some typos, but given the mathematical nature of this post, I’m less sure about this than usual. Anyway, here goes:
The best move in the cooperation game is Bob going to the airport, and Alice going to the beach, so that’s what’s played in real-life. The utility from the cooperation game is added to the maximin utility from the competition game (where beach/beach is played), for 100 Bob utility and 150 Alice utility. And so, the solution is that Alice goes to the beach and pays Bob 50 bucks to go to the airport.
Like, if the surplus-maximizing option is one that player 1 values at +80 dollars over the disagreement point, and player 2 values at +40 over the disagreement point, for +120 dollars of surplus value, the CoCo solution is that particular option is picked, and player 1 gives player 2 20 dollars, so both sides walk away with +60 dollars worth of utility.
So if I understand the second example correctly, doesn’t that imply that in the first example, Alice should only pay Bob 25 bucks so they both have 125 utility?
Anyways, the value that player i gets is the sum of the values it gets from all of the component games where coalitions compete against each other.
→ the sum of the values they get from
Finally, there’s lots of math about set differences. I believe in all these cases, using / as the symbol for a set difference may be wrong (?) or at least unconventional, and should be \ instead.
[These aren’t necessarily in order:]
[The first two LaTeX formulas for Shapley values, following the sentence “then the payoff for player i is”]
S⊆N/{i}
the subset N/(S?{i}),
For the game with S vs N/S
in the coalition N/S
[In the two latex formulas after the sentence “producing a restatement of the Shapley value as”, plus once after the sentence “But remember, the Shapley value can be re-expressed as”]
v(N/S)
and v(N/S) is the value of the opposing coalition
Loved this post, thanks for writing it.
I believe I’ve found some typos, but given the mathematical nature of this post, I’m less sure about this than usual. Anyway, here goes:
So if I understand the second example correctly, doesn’t that imply that in the first example, Alice should only pay Bob 25 bucks so they both have 125 utility?
→ the sum of the values they get from
Finally, there’s lots of math about set differences. I believe in all these cases, using / as the symbol for a set difference may be wrong (?) or at least unconventional, and should be \ instead.