Push Hands Is Not A Competition
One can find videos on Youtube of 'competitive push hands', where people are energetically playing a kind of standing game of tag crossed with a weak counterpart of sumo wrestling. The aim is something like getting your opponent to move their feet while keeping your own in place. Something like that, but it doesn't interested me to learn more. All that matters to me is that it isn't Taiji, and that winning a contest is not the point of Push Hands.
Push Hands exercises are exercises within which one aims to take the same Intention Driven Movement idea (and the various principles of posture and efficient movement) that one practises in the Form, and do the same while one's posture is subjected to external perturbation. That is, in the solo Form, one learns to do Taiji in the absence of external perturbations; practising a Taiji Form in a group then adds an external source of timing—there is an added aim of making the same postures and transitions in time with everybody else; in Push Hands, one aims to stand and move in the same way, while someone is gently trying to push you.
With time, the degree of external perturbation that one can tolerate increase, until eventually (in the case of a few masters), the results are fast enough, accurate enough, and robust enough, that one has something with which to build a martial art (Taijiquan).
But to come back to the title: the point of push hands exercises is not 'to win'. Whether or not you 'successfully push your opponent' is irrelevant: what matters is what you learn from the exercise, and how that learning enables you to transform yourself. Taiji is an art of self-transformation, more than anything else. The martial art side is secondary to this.