I don't see this as a man vs. woman issue at all. There are men with low self-esteem and there are women with low self-esteem. If people would make the effort to be honest with themselves, a lot of the superficial game-playing would fall by the wayside.
Sure there are different messages sent by way of mass-media and popular culture as to what society's "expectations" are for a given gender-role, but since those expectations are skewed against non-monogamous relationships for ANY individual of ANY orientation, I'm hard-pressed to draw the conclusion that it's easier or more difficult for men or women to find suitable partners in a polyamorous context.
The grass is always greener over someone else's septic tank.