"Is it necessary when trying to eliminate bouncy Joists to use 3/4 inch plywood or can I use half-inch?"
Was the structure built to code? If so, there shouldn't be a bounce. I just built a two story 2.5 car garage using my own design. Prior to building I researched on line for building codes regarding joist spans for live loads. I found that, to meet code for my situation, I had to use 2x10x12s - 16"o/c - supported by 4 glued up 2x12x16s - which were themselves supported by 2 jack posts equally spaced down the length of the garage. There was no bounce prior to installing the 1/2" plywood and it's solid as a rock. The alternative was to use 14" high laminated I beams which was unacceptable.
If you're not concerned about walking on the deck you don't need to be as critical but I don't think that plywood, by itself, will give you the results you're looking for. Plywood may greatly reduce the amount of bounce but, if the framework was under-built, it may not be a satisfactory solution.