In what way did Sony ever think they could compete with Nintendo in the handheld market?

[S.T.A.G.E.]

What sells Nintendo is well known and heavily marketed mascot characters. Sony does not care for mascot characters not do they heavily market them. They need to create characters that could become a household name, transfer them to the Vita and give the console new life. Jak and Daxter, Rachet and Clank should be on full Vita detail and no longer be a console franchise. Sony could get second party to make them.