A problem I have with Shapley Values is that they can be exploited by “being more people”.
Suppose Alice and Bob can make a joint venture with a payout of $300. Synergies:
A: $0
B: $0
A+B: $300
Shapley says they each get $150. So far, so good.
Now suppose Bob partners with Carol and they make a deal that any joint ventures require both of them to approve; they each get a veto. Now the synergies are:
A+B: $0 (Carol vetoes)
A+C: $0 (Bob vetoes)
B+C: $0 (venture requires Alice)
A+B+C: $300
Shapley now says Alice, Bob, and Carol each get $100, which means Bob+Carol are getting more total money ($200) than Bob alone was ($150), even though they are (together) making exactly the same contribution that Bob was paid $150 for making in the first example.
(Bob personally made less, but if he charges Carol a $75 finder’s fee then Bob and Carol both end up with more money than in the first example, while Alice ends up with less.)
By adding more partners to their coalition (each with veto power over the whole collective), the coalition can extract an arbitrarily large share of the value.
My concern is that if Bob knows that Alice will consent to a Shapley distribution, then Bob can seize more value for himself without creating new value. I feel that a person or group shouldn’t be able to get a larger share by intentionally hobbling themselves.
A problem I have with Shapley Values is that they can be exploited by “being more people”.
Suppose Alice and Bob can make a joint venture with a payout of $300. Synergies:
A: $0
B: $0
A+B: $300
Shapley says they each get $150. So far, so good.
Now suppose Bob partners with Carol and they make a deal that any joint ventures require both of them to approve; they each get a veto. Now the synergies are:
A+B: $0 (Carol vetoes)
A+C: $0 (Bob vetoes)
B+C: $0 (venture requires Alice)
A+B+C: $300
Shapley now says Alice, Bob, and Carol each get $100, which means Bob+Carol are getting more total money ($200) than Bob alone was ($150), even though they are (together) making exactly the same contribution that Bob was paid $150 for making in the first example.
(Bob personally made less, but if he charges Carol a $75 finder’s fee then Bob and Carol both end up with more money than in the first example, while Alice ends up with less.)
By adding more partners to their coalition (each with veto power over the whole collective), the coalition can extract an arbitrarily large share of the value.
Adding a person with veto power is not a neutral change.
I’m not sure what you’re trying to say.
My concern is that if Bob knows that Alice will consent to a Shapley distribution, then Bob can seize more value for himself without creating new value. I feel that a person or group shouldn’t be able to get a larger share by intentionally hobbling themselves.