Most people know the answer to that age-old question is “one slice/piece/bite at a time.” How do you attack an intrenched, big competitor? Same way.
In the 1960s Crest became the defacto cavity fighting toothpaste due to their unique acquisition of the American Dental Association Seal of Approval. This helped them achieve greater than 50% market share. There are MANY reasons to brush your teeth, and Crest no longer has 50% market share. Each “reason” sliced away market share.
It is no different today except that you also don’t need retail shelf space to take your piece. According to an article in Advertising Age, the big CPG (Consumer Packaged Goods) companies have lost 1.6% market share to “elephant eaters” in the last few years. You may scoff at 1.6%, but it equates to about $10B in sales, which creates a number of profitable companies.
One of the weaknesses of big companies is that it takes large revenue to get their attention. If your idea is only worth $50M in revenue, it may not even get the attention of the assistant to the Associate Product Manager at a big CPG company, but it can create a very profitable business for an entrepreneur.
As the article notes, these small opportunities carve away at the “elephant.” From a business strategy viewpoint, it reinforces the opportunity for companies to focus on ever smaller niches that can result in highly valuable products that are below the radar of big competitors. It has the further advantage that if it does become big enough to be on their radar, your company could then be an acquisition target for the big company; resulting in a nice pay-day.
Focus on building your market from small groups of customers not by trying to artificially segment a large market.