Yeah, the group dynamics of, say, a family with two children:

   1. Kid A plays with Kid B
   2. Kid A plays alone and Kid B plays alone

As compared to a three-child household:

   1. Kids A, B and C play together
   2. Kid A plays with Kid B, Kid C plays alone
   3. Kid A plays with Kid C, Kid B plays alone
   4. Kid B plays with Kid C, Kid A plays alone
   5. Kid A, Kid B and Kid C all play alone

So, in a bigger family, many more communication patterns between children can arise, which, among other things, might develop the child's empathy etc.

Adding mom and dad as "players" would give us many more possible scenarios here (Kid A playing with mom, Kid B alone or with dad, etc).

I'm a father of two with a low income, and I would like to have a third child for precisely the above described reason. As a sociologist in my country put it -- somewhat harsh words maybe, but probably largely true: a single child might get spoiled, two children may start competing too heavily, but three children and above is company.