Not the most airtight examples. Dropbox was first to market with an innovative service, they've been losing market share ever since Google Drive which now has 25%+ of the market. Netflix was also an innovative service that was first to market. So now there's a new monopoly type of a company who dominates a new market > cable tv.
Smaller company can't oust bigger ones unless it is actually possible for them to #1. Out innovate and implement a better service and #2. Hope the monopolies don't catch on to your idea and overwhelm it with their resources (i.e what Blockbuster could have done by adapting an online model). Those 2 critical circumstances don't have all that often.