You can make it work without an explicit veto. Bob convinces Alice that Carol will be a valuable contributor to the team. In fact, Carol does nothing, but Bob follows a strategy of “Do nothing unless Carol is present”. This achieves the same synergies:
A+B: $0 (Venture needs action from both A and B, B chooses to take no action)
A+C: $0 (Venture needs action from both A and B)
B+C: $0 (Venture needs action from both A and B)
A+B+C: $300
In this way Bob has managed to redirect some of Alice’s payouts by introducing a player who does nothing except remove a bottleneck he added into his own playstyle in order to exploit Alice.
Shapley values are constructed such that introducing a null player doesn’t change the result. You are doing something different by considering the wrong counterfactual (one where C exists but isn’t part of the coalition, vs one when it doesn’t exist)
Sounds like you agree with both me and Ninety-Three about the descriptive claim that the Shapley Value has, in fact, been changed, and have not yet expressed any position regarding the normative claim that this is a problem?
You can make it work without an explicit veto. Bob convinces Alice that Carol will be a valuable contributor to the team. In fact, Carol does nothing, but Bob follows a strategy of “Do nothing unless Carol is present”. This achieves the same synergies:
A+B: $0 (Venture needs action from both A and B, B chooses to take no action)
A+C: $0 (Venture needs action from both A and B)
B+C: $0 (Venture needs action from both A and B)
A+B+C: $300
In this way Bob has managed to redirect some of Alice’s payouts by introducing a player who does nothing except remove a bottleneck he added into his own playstyle in order to exploit Alice.
Shapley values are constructed such that introducing a null player doesn’t change the result. You are doing something different by considering the wrong counterfactual (one where C exists but isn’t part of the coalition, vs one when it doesn’t exist)
Sounds like you agree with both me and Ninety-Three about the descriptive claim that the Shapley Value has, in fact, been changed, and have not yet expressed any position regarding the normative claim that this is a problem?