It's hard to believe how badly Sony bungled the console market after the domination of the PS2.
They bungled the PS2 as well, it's just momentum from the PS1 kept it going.
When the PS1 came out it was powerful and simple. You wrote software in C, the libraries did everything for you. Compare this to the Saturn where you had two cpu's sharing the same memory bus, so you had to write your code so that it ran from cache as much as possible.
The PS2 was much harder to code for. Especially when compared to the xbox. The xbox came late to the market though, so developers were committed to it. Microsoft did a good job at getting people writing for it though, so by the end of that generation they were ready for the next.
Sega could have made more of an impact with the Dreamcast, but piracy killed the console stone dead. The gamecube was ok, but Nintendo wanted it to be a console for kids and while some games made it through anyway there weren't enough to build momentum.
With the PS3, Ken had gotten drunk on his own success. The PS2 hadn't deserved to be the success it was & the PS3 was even worse in term of complicated design. Plus they thought they could go it alone on a graphics chip. They were just going to implement a framebuffer, with the Cell actually rendering the graphics. At some point they gave up on the idea, it was obviously not good enough. Whether they gave up because of the time it would take to make it good enough, or whether they thought it could never be good enough I don't know. But they ended up going cap in hand to NVidia for a graphics chip.
It didn't help that Microsoft persuaded IBM to sell them the same CPU core that was going to be used in the PS3 and rather than using the Cell cores as well, Microsoft just specified that they wanted three of the CPU cores.
Sony also thought that when they clicked their fingers the developers would come running to write exclusive software. They had with the PS1 & PS2. However on the PS2 it was just because there were no other viable platforms at the time, on the PS1 it was because it was easier to write software. The 360 launched first, was easier to write software for than the PS2 & Microsoft courted the developers.
All that happened was Sony's luck ran out.