I do think we have seen that happen in practice with some of the "flag wars" of the past. One time I remember in particular, I was assuming that Steem's value was going up because two parties were both powering up to downvote each other. It's ironic that when that happens, the competitors strengthen each other by bidding up the value of their stakes.

OTOH, sometimes the target doesn't fight back, but instead they pack up and leave. That's harder to do when they're tied to an on-chain endowment, though.