Ok, I think I can articulate a reason for my doubt about the Shapley Value. One nice property for a fair division method to have is that the players can’t game the system by transferring their underlying contributions to one another. That is, Alice and Eve shouldn’t be able to increase their total negentropy allocation (at Bob’s expense) by transferring matter from one to the other ahead of time. Proportional allocation satisfies this property, but Shapley Value doesn’t (unless it happens to coincide with proportional allocation).
If such transfer of resources is allowed, your share of negentropy must depend only on your contribution, the total contribution and the number of players. If we further assume that zero contribution implies zero share, it’s straightforward to prove (by division in half, etc.) that proportional allocation is the only possible scheme.
This still isn’t very satisfying. John Nash would have advised us to model the situation with free transfer as a game within some larger class of games and apply some general concept like the Shapley value to make the answer pop out. But I’m not yet sure how to do that.
If such transfer of resources is allowed, your share of negentropy must depend only on your contribution, the total contribution and the number of players. If we further assume that zero contribution implies zero share, it’s straightforward to prove (by division in half, etc.) that proportional allocation is the only possible scheme.
One difficulty with proportional allocation is deciding how to measure contributions. Do you divide proportionately to mass contributed, or do you divide proportionately to negentropy contributed?
In Shapley value, a coalition of Alice and Eve against Bob is given equal weight with the other two possible two-against-one coalitions. Yes, Shapley does permit ‘gaming; in ways that proportional allocation does not, but it treats all possible ‘gamings’ (or coalition structures) equally.
Ok, I think I can articulate a reason for my doubt about the Shapley Value. One nice property for a fair division method to have is that the players can’t game the system by transferring their underlying contributions to one another. That is, Alice and Eve shouldn’t be able to increase their total negentropy allocation (at Bob’s expense) by transferring matter from one to the other ahead of time. Proportional allocation satisfies this property, but Shapley Value doesn’t (unless it happens to coincide with proportional allocation).
If such transfer of resources is allowed, your share of negentropy must depend only on your contribution, the total contribution and the number of players. If we further assume that zero contribution implies zero share, it’s straightforward to prove (by division in half, etc.) that proportional allocation is the only possible scheme.
This still isn’t very satisfying. John Nash would have advised us to model the situation with free transfer as a game within some larger class of games and apply some general concept like the Shapley value to make the answer pop out. But I’m not yet sure how to do that.
One difficulty with proportional allocation is deciding how to measure contributions. Do you divide proportionately to mass contributed, or do you divide proportionately to negentropy contributed?
In Shapley value, a coalition of Alice and Eve against Bob is given equal weight with the other two possible two-against-one coalitions. Yes, Shapley does permit ‘gaming; in ways that proportional allocation does not, but it treats all possible ‘gamings’ (or coalition structures) equally.