Is there an economic analysis of how piracy allows a product to take a hegemonic position? There's an interesting situation with the likes of Photoshop, where the software being pirated actually increases its market usage, and the software becomes the de facto standard, in part due to software piracy.

In the instance of Photoshop for example, it's likely that people creating funny doctored ('photoshopped') images and spreading them via the internet, were using pirated Photoshop software. 

Here's a Life Hacker article on it. 

What it means, is that especially for a creative software like Photoshop, or Ableton (music production software), the developers shouldn't make their copyright protection too strict. It should be easy enough to crack so that people can actually use it, but pain enough to get people to fork out if they're serious enough. 

My question is - is this a well researched phenomena in economics?

Is there an optimal either pricing strategy, or copyright protection strategy, that takes this into account?
The model is a variant on penetration pricing (effectively $0 for pirates) which is used to gain market share. 

The problem is while monopoly may be desirable, the path to monopoly is generally not, as the cost to acquire market share rises relative to the value of each additional unit of market share.

While there is no specific study of Adobe that I know of, penetration pricing and market share are generally well understood concepts in economics.

That being said while the linked MIT paper implies an "uncanny valley" of sub-optimal over-penetration before a monopolistic (~100%) market share/maximal profit scenario, to my knowledge the empirical data on ologopolistic firms and cartels is scant, outside of the energy industry. Historically, however, OPEC and the Seven Sisters, have never actually combined to a monopoly, nor engaged in penetration pricing by giving away oil (again, to my knowledge).

One thing that is agreed on is that a monopoly is only as valuable as the barrier to enter the market (broadly speaking).

Combining those facts one could surmise that for Adobe to maximize profits they would need to choose a strategy that allowed for either:

a) optimal penetration 

$$or$$

b) monopolistic dominance of an industry that would need to produce profit per year less than roughly the barrier to entry divided by the discount rate they erected through a combination of R&amp;D costs and $0 penetration pricing strategies. 

$$P_{Total} &lt;  \frac{B}{r}$$

Monopoly of a more valuable market would entice a rational actor to break it and leave both in the sub-optimal valley of oligopoly (unless they colluded), hence the prevalence in niche technical markets you mentioned. 

Not to say graphic design is a small niche, but of the population at large they represent rouhgly 0.08% (at least in America).