I just think this example is misapplying the Shapley values/approach—in a case in which a payment is locked in, there is nothing in the Shapley approach saying you would treat it as if it is not locked in. As a matter of principle the Shapley values are order invariant, but that is not to say that when computing Shapley values you should imagine an alternative reality in which everything is order invariant when in fact it is not. As described I think the Shapley values in this case naturally argue for the second actor to favor getting the 15 units by completing the payment for P.
Here is how I would think this situation would be computed using Shapley values:
Whereas if player 2 were to aim for just going for their single better option, it would be:
So if player 2 seeks to maximise their Shapley value, they do in fact choose the option you think that they should.
So I think it is correct that one should consider if commitments are locked in etc., but I don’t think this is a critique of the Shapley approach, but rather that what is described as a ‘simple application of the Shapley values’ is just an incorrect application.
I just think this example is misapplying the Shapley values/approach—in a case in which a payment is locked in, there is nothing in the Shapley approach saying you would treat it as if it is not locked in. As a matter of principle the Shapley values are order invariant, but that is not to say that when computing Shapley values you should imagine an alternative reality in which everything is order invariant when in fact it is not. As described I think the Shapley values in this case naturally argue for the second actor to favor getting the 15 units by completing the payment for P.
Here is how I would think this situation would be computed using Shapley values:
Whereas if player 2 were to aim for just going for their single better option, it would be:
So if player 2 seeks to maximise their Shapley value, they do in fact choose the option you think that they should.
So I think it is correct that one should consider if commitments are locked in etc., but I don’t think this is a critique of the Shapley approach, but rather that what is described as a ‘simple application of the Shapley values’ is just an incorrect application.
Mmmh, good point