Considering Perdiccas' long service under Alexander and the promotions he received in the king's service, I think it's safe to assume that he was not at all stupid. He was not Alexander though, and could not call upon the same ties of loyalty the king could
Not stupid, but there's no denying that Perdiccas had nearly every advantage in the beginning and blew it one by one as mentioned above.
When Alexander died, he had:
A) The core of the army
B) The veteran bodyguard corps (infantry and cavalry)
C) Alexander's body
D) The treasury
E) Physically at the core of the Empire
F) Some form of legitimacy from being the regent/supposedly the one Alexander gave his ring to
He ended up losing all of these, piece by piece, only to be murdered by his own ambitious officers after having made enemies of almost everyone and with really having only gotten rid of one rival at the start.
As a sidebar/plug, I really like this period and heavily recommend
Marshals of Alexander's Empire - Waldemar Heckel. It made understanding the individuals involved much easier and especially made it easier for me to keep the Cleitus' distinct (the Black and the White!)
It even mentions available information about more obscure officers, like (I wish I had the book here to write it out...) the top 3 winners of the 'martial skills' contest held by the army just after the Babylonian campaign ended, before they went to northern Iran/India, etc.