Anecdotally I found my performance to - both in the gym and in the office - increase not decrease. From athletes and academics I follow on social media, they also say the same. I've read a few hypothesis as to why this may happen. In an evolutionary sense, when in a fasting state we would require more energy to go out and hunt/gather food to take us back out of that state. IIRC, metabolism increases while fasting. It wouldn't make sense for our body to reduce performance because that just makes starvation an even more likely possibility, as it suddenly becomes much harder to go out find a food source due to said >"major performance decrease".
There are a few studies knocking around about regarding it, but I've only got a minute so this is the best I could do for the moment-
"Findings indicated that pre-exercise feeding enhanced prolonged (P = .012), but not shorter duration aerobic exercise performance (P = .687). Fasted exercise increased post-exercise circulating FFAs (P = .023) compared to fed exercise."[1]
There are a few studies knocking around about regarding it, but I've only got a minute so this is the best I could do for the moment-
"Findings indicated that pre-exercise feeding enhanced prolonged (P = .012), but not shorter duration aerobic exercise performance (P = .687). Fasted exercise increased post-exercise circulating FFAs (P = .023) compared to fed exercise."[1]
[1]https://www.ncbi.nlm.nih.gov/pubmed/29315892