Hmm...I can't remember for sure.
In the 80s, my dad bought us games. I remember my brother saving up a bunch of money to buy a Gameboy and some games at launch in '89. I got one in 1990 and I must have bought something for it. We didn't get an NES until late 1990 and my dad bought us a shitload of games since we'd find so many on the cheap. I know I bought TMNT II The Arcade Game with my own money. I'd saved for months and freaked out when a kid brought the manual to school. Had no idea it was out and couldn't think about anything other than racing home and begging my dad to take me to go get it in the afternoon.
I do remember buying Metroid II on the Gameboy in 1991- it was only $19.99 at release and I'd saved up enough allowance to buy it outright. My parents were kind of pissed because they clearly had bought it for me for the holidays but couldn't say anything about it.
I also remember buying Double Dragon on the Gameboy but I can't remember which one of those came out first.