"An Imperial Affliction"
An Imperial Affliction, unlike most of the books and poems referenced in The Fault in Our Stars, does not really exist. While allusions to real literature can be revealing, a book created entirely for the purpose of existing within Hazel's world is of even more interest. Hazel likes the book because it is about a girl with cancer, allowing her to relate and empathize, but is not a "Cancer Book" in that the girl is not presented as the most strong and amazing person ever and does not start a charity that is cancer-related, instead creating The Anna Foundation for People with Cancer Who Want to Cure Cholera. Hazel seems to like the book because she approves of the girl in the story not allowing herself to be defined by her cancer. Furthermore, some of what draws Hazel (and Augustus) back in is the brutal lack of ending, demonstrating their reasonable mutual interest in childhood death and what happens after for the child and especially the world around them (hence their fixation on what happens to the Dutch Tulip Man and Sisyphus the Hamster.
The Unlit Cigarette
Gus's unlit cigarette is a clear symbol, even to him who chooses to do it for that reason. It is almost masochistic, like wanting to love Hazel even when he knows about her illness, keeping something that could hurt you so close. However, from the way he explains it outside of their first Support Group meeting together, he seems to see it more like holding the power over something that could make you sick, betraying his desire for control and agency.
The Swing Set
The day that Augustus and Hazel give away the swing set online is the day she allows herself to fall in love with him (though she doesn't tell him yet). The swing set as a symbol is a strong one, hearkening back to a generalized and likely idealized childhood in which she was young, cancer-free, and able to play un-tethered to an oxygen machine. Hazel acknowledges that she has no strong specific memory there, but that seeing it makes her sad in general. Furthermore, with Hazel's main issues with living and dying being the impact she makes on her parents and others, it makes sense that she would want to get the reminder of her childhood away from her parents and attempt to make a positive impact on another family while she can.
"The Price of Dawn"
As a book series and a video game, The Price of Dawn is attractive for its simplicity, high body count, and - unlike An Imperial Affliction - its lack of ending. Like the gory movies Augustus and Hazel watch together as well, Augustus seems much more into these hyper-violent movies, books, and video games because they allow the watcher or reader to witness and experience valor and martyrdom. Isaac specifically says what is wrong with Augustus and The Price of Dawn's video game, which is that Augustus is so blinded by saving someone on the small-scale and making a mark that he can forget the rest of the game and therefore can't accomplish the goal that will allow the person to actually be saved. This is symbolic of the blinding effect this same ideal has for Augustus in real life, not allowing him to appreciate what he has and who he is. Finally, by tracking Augustus's ability to play and engage with the game, the reader can track his quick deterioration in body and spirit, since it is clear even to Augustus that what he always wanted from the game was the action and valor he eventually finds pointless in his last days.
Peter Van Houten's House
Peter Van Houten moved to Amsterdam after his daughter died and he wrote An Imperial Affliction based on her life and death. Therefore, his house was set up to be a haven from him, protecting him from memories of her and from contact by his fans who loved the book written for/about her and thus remind him of her as well. After living there for 18 years, his house looks almost un-lived in, with almost no clutter, likely because all he seems to do is drink and think. However, in his living room there are two trash bags of letters from his fans. These trash bags of letters in an otherwise spotless house represent the facts that he cannot get away from his daughter and that he doesn't want to. It is as if he has tried to throw them out, even putting them in the trash bags, but simply cannot let go.