If B1 and B2 structure their cartel such that each of them gets a veto over the other, then the synergies change so that A+B1 and A+B2 both generate nothing, and you need A+B1+B2 to make the $100, which means B1 and B2 each now have a Shapley value of $33.3 (up from $25).
Also, I wouldn’t describe the original Shapley Values as “no coordination”. With no coordination, there’s no reason the end result should involve paying any non-zero amount to both B1 and B2, since you only need one of them to assent. I think Shapley Values represent a situation that’s more like “everyone (including Alice) coordinates”.
If B1 and B2 structure their cartel such that each of them gets a veto over the other, then the synergies change so that A+B1 and A+B2 both generate nothing, and you need A+B1+B2 to make the $100, which means B1 and B2 each now have a Shapley value of $33.3 (up from $25).
Also, I wouldn’t describe the original Shapley Values as “no coordination”. With no coordination, there’s no reason the end result should involve paying any non-zero amount to both B1 and B2, since you only need one of them to assent. I think Shapley Values represent a situation that’s more like “everyone (including Alice) coordinates”.