For innovation (patents and technology) I would suggest "identify and target potential market entrants". Highest market share doesn't mean that they are doing everything innovative. And highest market share is not a lifelong thing. It keeps changing. Market share goes to the innovators and early adopters of technology. Of course, a lot of other factors matter too. Few examples - 
1. Yahoo was once market leader but now lost to Google. 
2. Nokia and BlackBerry were the synonyms of the mobile, but now?

It all depends on what you have to offer from an IP perspective. All of the situations are the same because each one is unique. Over 85% of my former employer's revenues comes from businesses, products, IP and technologies that have been acquired and they are a global leader in many of their served health care market segments and have been for over 90 years.. Their brand name recognition in health care is comparable to Coke in the consumer market and the brand power is simply amazing in supporting a global product launch and reaching every conceivable market segment.

Choosing the new market entrant approach comes with a difficult challenge. You first need to convince the target that this is a new market opportunity for them. This takes both time and money that may be avoided by partnering with a market leader. I have seen actual examples of a market leader evaluating a potential partnership with a technology company only to watch the technology company recognize the huge market opportunity and enter the business themselves against theit potential partner.

It all depends on what you have and the partnership that makes the most sense from a strategic and financial perspective for your particular IP/technology opportunity.

As mentioned by Hitest for innovation I will target market entrants. Monopolist does not match with innovation. Generally speaking I would study the market monopolist but with the goal of finding missing opportunities and a niche to enter into the market.

Looking at the 5 forces of Porter defining the competition, 2 important ones the power of new entrants and the power of substitution. Regarding new entrants, one of the big exemple of all times was Kodak who died while it was very rich as they never thought digital photo would replace argentic. The had plenty of patents and reacted by inventing a new argentic format called APS. For substitution, you have the UBER / Taxis. You can also call this disruption. So you would definitely not target the company with the highest market share... but be careful the FTO which by the way should not be a problem if we are in presence of a disruption.

From my experience and actual real life business examples, the monopolist can and does embrace innovation and execute the necessary tactics required to educate a market on new technology or a solution to a problem not yet recognized by the the customer. Market education, particularly in the health care industry is time and investment intensive. This effort is compounded when it becomes global in nature, but the rewards are well worth the effort in revenue, retaining market leadership, competitive advantage and continuing to support the brand strength and recognition as an innovator.