Here in Hawaii the kids generally use the Japanese term, Jan Ken Po. Take a look at this site for some history and alternative games, including versions from all over Asia. This Cantonese version is a bit complex:

The Cantonese people of China play not a sansukumi but a gosukumi game [i.e., 5 choices instead of 3]. The symbols are god, chicken, gun, fox, and termite. God is the thumb, chicken the index finger, gun the middle finger, fox the ring finger, and termite the little finger. The sukumi relationships are like this: with God and Chicken, chicken is sacrificed to god and thus loses. With God and Gun, the gun introduces people to god(?) and thus God wins. The termite eats the God's statue, and thus wins. The gun defeats the chicken. The fox defeats the chicken too. The chicken defeats the termite. The gun defeats the fox. Other than that, the god and the fox are good freinds, as are the gun and termite, and the fox and termite take no notice of each other, so these symbols tie with each other. According to these rules, the god and gun are strongest, and the chicken weakest.

Got it?

Aloha,
Mark

(still trying to figure out the one from China called "Hammer, Scissors, Bomb"...)