I have observed that in family games of the board game "Acquire", I would typically play solidly and take very few risks while my father and brother would play solidly and take a lot of risks. (There was also my little sister who was a little too young to understand the game, she just didn't play very well at all) This led to me always getting second place and my father/brother trading first and third places among them.

I never thought about it as maximizing max payoff vs maximizing min payoff but it makes a lot of sense. I also observe this behavior in other areas of our lives.