There are inhibitory neurons in every layer (but I'm not sure if that's true for every region/species).
However, that doesn't mean every layer does competition. Inhibitory interneurons are really varied, maybe even more so than excitatory neurons. They probably have lots of functions, so it will be hard to determine which types are involved in competition.
There is probably competition in multiple layers because temporal pooling involves competition. But I've also heard that columns extend through all layers, which would seem to suggest that all layers share the same spatial pooling.
Here are a couple sources which could help. Neither says much on competition though. Maybe someone else knows of papers more specific to your question.