Our situation is complicated - but I chose 'her idea' for a variety of reasons. It is closer to say "both" - my wife has never been successfully, or happily monogamous, and cheated on me even during the years we were dating. I did not find out about those affairs until later in life, when we had been engaged, broken off our engagement, then resumed it. During that time I became obsessed with the idea of her fucking other men.
After we were married, once again my wife had a half-dozen or so affairs, some of which I found out about, or was suspicious, some of them I had no idea. But she never was open about it, and rejected the idea of fucking other men in the "hot wife" sense, other than responding to the notion during sex and fantasy role-play.
After our kids left home, things changed, and she began moving in that direction, finally one night, unplanned, and to my complete surprise she acted on it, and fucked a guy that she'd picked up in the hotel bar, right in front of me, more or less oblivious to my presence. From that point on, we have been actively doing the hot wife thing, and we both love it.