There's not much to say about Anthony and Nick other than forget Anthony and Nick.
These guys are older brothers, plain and simple. After an already nasty day, Anthony "makes" Alexander fall in the mud, and Nick calls him a "crybaby."
More than for other characters, the illustrations tell us a lot about these two boys. As Alexander mopes about his boring white sneakers, the illustrations show Nick sitting pretty in his red ones with white stripes and Anthony smugly tying up a nice shiny pair of white ones with red stripes. Even before they start picking on Alexander for real as part of the written story, the illustrations show a braggy Anthony smiling and holding up his awesome Corvette Sting Ray car at breakfast while Alexander holds his head in his hands.
So…do Anthony and Nick have their little bro's back? Do they lift him up when he's down? No. The opposite, actually. Anthony looks like he holds Alexander down in the mud while Nick taunts him. So, yeah, these guys aren't exactly supportive or empathetic older siblings.
And just like in real life, they don't change over the course of one day. They'll probably pick on the little guy tomorrow, too.
Brothers are just like that. Even in Australia.