3/32" vs. 1/8" riding fixed

single speed or fixed is no no to have a 3/32 chain, an 1/8th is THE only one to have- it doesn't have the sideways flex the 3/32 has to have on geared bike: its not called derailure chainfor nothing,its capable of being derailed off one sprocket onto another.

3/32" chains do not supernaturally leap off chainrings. Chainline and tension are much, much more important than width.