Indistinguishability game hop I am trying to prove that changing an input in a security game from a randomly permuted set to a set that is permuted using a pseudorandom permutation (PRP) results in a negligible distinguishing advantage between the two games. Does anyone know of any good examples in the literature of this kind of game hop. I have already read through the Shoup 2006 paper on games.
While I cannot point you to a specific paper that works as a great example for this technique, the idea is quite simple.

Assume two distributions $X,Y$ which have the same support, so random variables distributed according to one of these distributions are drawn from the same set.
Now assume you got a probabilistic adversary $A$ that takes as input $misc$ and a value $x$ that drawn according to $X$ and tries to solve some problem. Here $misc$ covers any additional inputs. As $X$ and $Y$ have the same support, we might also chose $x$ from $Y$ -- $A$ should at least accept such $x$ as input. 

Let's switch to the games. Assume you got two games. In both you generate $misc$ the same way. But the games differ in how $x$ is chosen. In game 1 you chose $x$ according to $X$, in game 2 you chose $x$ according to $Y$. You might already see that if the success probability of $A$ differs, depending on if he plays in game 1 or in game 2, we can use this to distinguish the two cases, i.e. we can use this to decide from which distribution $x$ was chosen. 

Say $A$ wins in game 1 with higher success probability than in game 2. Then we can built a distinguisher $D$ that takes a value $x$ and outputs 1 if $x$ was chosen from $X$ and $0$ if it was chosen from $Y$. $D$ simply runs $A(misc,x)$ and outputs 1 if $A$ succeeds. $D$ will distinguish the two cases exactly with $A$'s difference in success probability depending on which game he plays.

Hence, we can argue that if $X$ cannot be distinguished from $Y$ with probability greater $\epsilon$, the difference in $A$'s success probability between game 1 and game 2 must be limited by $\epsilon$. 

That's how one game hop works. You can extend this arbitrarily. The important thing is that between two consecutive games you must only change the distribution of one of $A$'s inputs.