The basic rule for sense selection in a tcas/tcas encounter is that before selecting a sense each tcas must check to see if it has received an intent from the threat . If so tcas selects the opposite sense (eg climb/descend). If not tcas swelects a sense based on the encounter geometry just as if the threat was nontcas eqipped. In the vast majority of cases 1 aircraft sees the other as a threat at different moments in time. Coordination proceeds in a straightforward manner therefore.
IF both see the other as a threat simultaneously and both select a sense based on geometry (practically impossible) the a/c with the higher mode S address (each airframe has a unique mode S address) detects the incompatibility and reverses its sense.
Don't ask about the three second delay to avoid confusing the pilot in this case; or tau, multiple conflicts, atcrbs, sensitivity levels, whisper shout, mode S message formats, etc.
It's impressively complicated!