You're probably right.
If not credits, then maybe ratings points. I've seen it done on other gaming sites where the higher rated player has more to lose and the lower rater player more to gain, therefore essentially creating a handicap sytem based on skill.
For example, if player A is a (70.0) and beats Player B who is a (75.0), Player A would improve by (.2 points), and therefore would become a 69.8, and Player B would become a 75.2. If Player B won, then he could gain (1.0 point), therefore improving to 74.0, whereby Player A would move to 71.0. The amount earned could be based on a formula derived from the delta of the two competitors.
Have I mentioned that I like wagering in golf? Think about it. You could play any different number of games (match play, skins, four ball, etc.).