If you are facing issues connecting to WiFi from your Play Station 3 and seeing error code 8013013d then here is the trick to make it work.
Go to your router settings and disable “WPS settings” and that should fix it.
Irrespective of whether you have this issue or not, it’s better to disable WPS(Wi-Fi Protected Setup) settings on your router. It’s a bad security setting that is easy to break and highly discouraged to not use it. Instead go with strong security settings like WPA2.
Most of the routers enable WPS by default.
Read more about WPS settings here.