Correct structuring of random effects?

#1
Hi

I have produced a mixed effects model as follows;

lmer(TotalPayoff~Type+Game+PgvnD*Asym+(1|Subject)+(1|Pairing),REML=FALSE,data=table1)-

each pairing contains 2 subjects and each Subject is in 2 different pairings with different subjects. Have I structured the random effects in the correct way to control for the non-independence of TotalPayoff between data from the same subjects as well as between data from the same different subjects in the same pairing? (If one subject in a pairing has a high Total payoff the other will too).

Thanks Jonathan