Did Tywin sleep with Shae out of pure spite?

In the context of Game of Thrones, Tywin Lannister's relationship with Shae is portrayed as a deliberate act to hurt Tyrion, his son. While the show does not explicitly state that Tywin slept with Shae solely out of spite, it is clear that his actions were intended to further humiliate and betray Tyrion. Shae's decision to align with Tywin was motivated by her own hurt and anger towards Tyrion, who had called her a "whore" and tried to send her away, as well as her jealousy over Tyrion's forced marriage to Sansa Stark1.

In the books, Shae's character is depicted differently; she is portrayed as opportunistic and self-serving, and her involvement with Tywin is not explicitly driven by spite but rather by her own interests1. However, George R.R. Martin has hinted at deeper complexities in Tywin's actions that might be explored in future books, though he has not elaborated on them1.

Overall, while Tywin's actions were certainly intended to harm Tyrion, whether they were purely out of spite is not explicitly stated in the show or books.