Final answer:
King Claudius has not acted against Hamlet due to the prince's popularity and the potential for social upheaval, as well as the complex familial relationships that his actions could disrupt.
Step-by-step explanation:
The question pertains to the reasons why King Claudius in Shakespeare's play Hamlet has refrained from taking action against Hamlet despite Hamlet's seemingly treacherous acts against him. The reason, as provided in various parts of the text, is multifaceted. Primarily, Claudius is wary of the love and admiration that the people of Denmark hold for Hamlet.
This popularity makes it dangerous for Claudius to openly act against Hamlet, as doing so could lead to social upheaval or pose a threat to his own reign. Moreover, Claudius is Hamlet's uncle, and his marriage to Hamlet's mother, Gertrude, further complicates the situation, as any action against Hamlet could disrupt familial bonds and the stability of the kingdom. Hence, Claudius is caught in a delicate political and personal bind that constrains his options concerning Hamlet.