To help answer the question of how to determine a brand's position, here are a few definitions and strategies to help with defining a brand's positioning and how to implement a positioning strategy.
Whilst there are various interpretations about what Brand positioning is, I'd like to sum it up simply as:
"The mental space you wish to occupy in the customer's mind" - when they think about your brand's products or services.
It takes the benefits you've identified and outlined within your value proposition design and making them meaningful to your customers.
So to determine the competition and it's potential, you simply have to do your research and understand who's occupying that space (the competition) right now (in your customers mind) and how your value proposition (brand message) can be deemed and experiences as a better option (value) than that of the competition.
And finally - promotions is not the same as brand positioning and marketing. Once you have identified your potential customer group(s) and created a persona strategy assuming you've done that, you will have a better understanding of how to engage your core target market. It will also help with identifying the appropriate demographic i.e.; who they are, their lifestyles, where they hang out, what motivates them to buy, how often and how much they spend. After that you can then design your promotional strategy or campaign to reach them.
Hope this helps as a starting point and feel free to connect if we can be of further help.