The goal of bargaining is not usually to give the other party the best possible (most profitable) outcome. Does this Nash BS take into account for the bargainer

The goal of bargaining is not usually to give the other party the best possible (most profitable) outcome. Does this Nash BS take into account for the bargainers that an agreement not reached will favor neither, or perhaps favor one less than the other. One party says to the other "your math is hogwater, no deal! We'll still build it some other way, but you won't get anything." Leverage is a simple machine.