Interpersonal theory is based on three strands, which serve also as principles that aim to explain the development of personality traits.
The first strand is complementarity. This principle assumes that people in relationships that is, couples, regardless of gender, negotiate with words and with non-verbal communication their role within the relationship. This is how you get the submissive/manipulative, master/servant dyad.
The second strand, statistical deviance, claims that a factor known as vector length decides the social success of individuals depending on how flexible they are willing to be with the environment that surrounds them, as well as with the people who interact with them daily.
The third assumption is that the factors that intervene in the human experience mold personality through a circumplex structure. In other words, life is quite complicated, complex and in constant change, for which flexibility of character is key to tolerate the changes.
In the case of a famous musician, such as Prince, we have a number of environmental factors and dynamics that are unique to someone who is a successful, public icon.
First, his environment is unlike the typical environment of the average person. While the average individual enjoys privacy and anonymity, someone like Prince is consistently bombarded by fans, paparazzi, photographers, and the media. This "bombardment" factor alone can make or break a person, molding their personality to a point where they avoid being easily approached. This is not snobbery; people have the right to protect themselves.
If a super-well known figure wishes to enjoy his rights and liberties in the community, he will need added security. With it, comes the tapering of dynamics: no longer can you trust everyone, nor can you just assume that people surround you out of pure admiration. The added security may keep a superstar safe, but then their approachability will render them subject to the opinions of their fans.
The environment of a well-known superstar is also part of their job. Hence, the pressure put on by the music industry to sell albums (which is the reason why Prince rebelled against the industry, writing the word "slave" on his face) combines with the need to sell an image: Prince may or may not have much say in what goes on as far as his public persona because super-musicians are given a publicist to take care of that. The lack of control that a superstar such as Prince may actually have over his own creativity could render him quite unhappy. This is a complaint made by fellow super star singer, the late Kurt Cobain. In 1993, Cobain denounced that the music industry builds the stars according to what the public wants to see, taking away much of the creative license from the artist. As a result, many stars of high caliber end up abusing alcohol and drugs.
We could add many more influencing factors that will mold the personality traits of a superstar, but the important thing to consider is that the three main paradigms of interpersonal theory are null in the case of someone that has limited access to traditional (and perhaps even healthier) social dynamics. When you and your circumstances depend on selling millions of dollars, a person such as Prince is no longer his own master; he is the employee and the product of his industry.