Well, some degree of bickering is to be expected between siblings of that age, but you really should consider going to a professional who can assess the situation to it's specifics, if your afraid things might get out of reasonable control.

Anything I say here would obviously be to generic, and you might probably already know. At any rate, one quick trick to get your kids to stop competing amongst themselves is to have them compete with some 'outsiders' - take them to a family outing game of Frisbee or whatever to compete against their cousins or neighbours or someone else. Outgroup becomes ingroup really fast in these situations, and your family unit becomes a team.