Your BATNA often is directly correlated with your reservation point, which means it's incredibly important to the deal you ultimately reach. The better your BATNA, the better off you'll be. Since your BATNA is always in flux, you should constant seek out new opportunities to improve it.
It's important that you do not share your BATNA except in specific situations, since it's often closely tied to your reservation point. In general, you'll reject any offers that are worse than your BATNA and accept offers that are better than your BATNA, so you don't want to give away this valuable information to the other party. However, the following two cases are exceptions to this rule: