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playing tug of war in space, who wins

what would happen if I played a game of tug in space? I'm considering the gravity to be zero and the mass of the rope is negligible and there is no friction. My mass is larger but the force with which i'm pulling is less than that of my lighter yet stronger opponent.

I'm envisioning that we both move towards the center and no one wins, or is the person with the larger mass always going to win. I cant quite wrap my mind around all the possible scenarios.

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