While only monopolies win (whatever the micro-market they serve), there's no simple way to identify one. In fact, monopolies might constantly try to hide the fact that they're a monopoly (read this article for Peter Thiel's examples on the topic). So how do you validate how well your startup is doing with respect to the goal of being a micro monopoly?

Here's a good, simple way:

Can your company identify all the customers of an incumbent player serving a similar or overlapping need, and capture market surgically? In other words, can the company steal clients from incumbents easily in (at least) a segment of the market? 

In simpler words, can you fruitfully follow a "see bear, shoot bear" strategy?

If a company can 'see a bear, shoot a bear' consistently - even if it's within in a small niche segment in a larger industry - there's a signal of success in there. However, this method is a litmus test or post-facto analysis, so: If your company can't see a bear, shoot a bear, best to work on either the product or the value proposition until you can.

P.S: Recently got this wisdom from the COO of a fast-growing SaaS company here in San Francisco. Salesforce, famously, followed the same strategy against Siebel. Do check that story out here.