What do you think would happen if two people try to Summon the same thing at the same time?

Kind of echoing what pink_faerie81 said, I suppose it works the same way as when two spells (i.e. Voldemort and Harry's big face off in GoF) collide with each other. The stronger wizard - whether that means stronger in magical ability, in willpower, etc - would cast the Accio that wins out against the weaker one. Although you can't see the Accio spell in the same way that you can see a hex/curse when it's casted (you know, the ray of light type thing *is eloquent*), it's still a spell, and so I think it would just work the same way.

Cami {Ravenclaw}