In today's world, innovations seem to burst onto the scene from many producers indicating simultaneous inventing or at least copying activity from multiple players. For instance, right now multiple players are racing to produce an autonomous car. Just a few years ago, motion-trackable wrist-mounted devices exploded onto the market.
In the past, for most major inventions which we tend to attribute to a single inventor, like Edison with the light bulb or Ford with the Model T, were there multiple inventors racing to be the first to solve a well known problem or was the invention a solution brought forth by a lone creative inventor? What did the competitive environment look like? Additionally, was there a flood of competitive products that were introduced?
Funny that you mention that 'we' attribute the light bulb invention to Edison as this is one of the most well known misattributes in modern (Western) history. To me it's in the same group as Columbus discovering the Americas and 'everyone' used to believe the earth was flat.
That aside, it's true that in pre-corporate times most inventing was done in small settings, often by individuals with perhaps aids or assistants. The 'master' then published its results and usually got credited. Of course this was often bounded by financial means, so naturally when companies could finance research, inventions tended to shift to research groups. Good examples of these are almost all electronic inventions since the second world war like the microchip and the compact disc.
Nowadays we live in a much more complex technology, so it's no longer one 'thing', but more of set of features completing each other. Think of autonomous vehicles and augmented reality.