What if Putin threatens us with war over Alaska?

This isn’t related to the core enumerated powers questions in Bond but struck me as sufficiently interesting that it was worth posting about separately. In his post about Bond, Mark Tushnet writes:

[T]his isn’t Justice Thomas’s problem but James Madison’s [but] Justice Thomas quotes Madison to the effect that treaty cannot “dismember the empire.” Really? Suppose Vladimir Putin lets the United States know that he’s going to bomb the bejeezus out of the “red” states of the United States unless we negotiate a treaty returning Alaska to Russia. Work out the scenario as you wish, but I doubt that it’s a good constitutional design to require the U.S. government to take the negotiating position, “We’re fine with giving up Alaska but unfortunately we can’t do it, so bomb away.”

I don’t know what the optimal constitutional design is, but I confess that my intuitions are the opposite of Tushnet’s. Presumably the rule only has bite if a state does not consent to being turned over. (The Constitution requires the United States to “protect each” state “against invasion” and elsewhere requires state consent to interstate reallocations of territory.) Under those circumstances, would it really be such a bad idea to promise to each state in the union that we won’t sell them out to foreign powers?

I would have thought that a very simple game-theory cooperation model could plausibly provide that it’s rational for all of the states to promise to protect one another against foreign enemies. After all, that is part of what makes it safe for states to provide money and land and personnel to the federal government. If there were a serious risk that the rest of us would sell Alaska out to the Russians, presumably Alaska would have wanted to hoard assets and invest in a bigger militia.

And of course, if we were serious about keeping our constitutional commitments, and Putin knew it, would he have any reason to follow through on his threats?