Following the aesthetics-challenge my first question on this site:

In several episodes of "The Big Bang Theory" Wil Wheaton appears. 
![enter image description here](https://i.stack.imgur.com/i1R4k.jpg)

In the credits it is stated that he plays "himself". But I have problems with that statement. It seems to me that there are two different entities: The **A**-ctor on the set of Big Bang Theory and the **C**-haracter he portrays. They must be different entities because they have different properties: **A** has no friend named Sheldon Cooper. **C** was never actor in a show named "The Big Bang Theory". So following Leibniz **A** and **C** cannot be the same entity.

But there are very strange consequences of this. For one the character he plays is said to be Wil Wheaton. If someone asks me, which character is played by Liam Neeson in "Schindler's List" I would answer "He plays Oskar Schindler, a historic person of the third Reich". Accordingly if someone asks me which character is played by Wil Wheaton in "The Big Bang Theory" I'd answer "He plays Wil Wheaton, an actor known from Star Trek". I would not answer "He plays a character very familiar to Wil Wheaton". If a character in a show is introduced as Mr. So-and-so he *is* Mr. So-and-so, not a character very similar to Mr. So-and-so. If we need to drop this "rule", we were also forced to say: "In Skyfall Daniel Craig plays a character similar to James Bond." That sounds most weird to me. And it feels wrong. 

Also with this approach we create a whole new set of entities: To every **C** there is also an **A** then, and that's not exactly ontological parsimony.

Are there any theories dealing with cameo-problem? And if so: How is it dealt with?