The improv actor should always be willing, but never wanting.
Simple, yet profound. Always accept whatever is happening around you, and never force your ideas on your partners.
Obviously, almost the opposite counts for your improvised characters. They should have a clear objective and give at least some resistance to change, in order to become real and compelling.
The contradiction between actor and character is often huge. When somebody shouts "Please, don't go!" at you on stage, the actor behind that character probably wants you to leave. And when you hear "I'm leaving you now.", that actor might be signalling you to try and make the character stay.
Yet, as an improv actor: be willing, but not wanting.