There is a newly published book entitled Collusion by Omission. While the contents deal with a different aspect of modern politics, there is a similarity in that by the omissions of any objections to the affairs of state, the party in question is in collusion with that state. Thus, in Hamlet, the king commands great power through the collusion of his court, as well as by the very nature of his ruling position. When, for example, he orders the school friends of Hamlet to spy upon him, they do not demur because the skillfully manipulative Claudius convinces them that he wishes to learn what troubles Hamlet as, for instance, in Act III, Scene 3, he tells them that it is detrimental to the stability of the state for Hamlet to be observed in his derangement:
...nor stands it safe with us
To let his madness range. Therefore prepare you....
And he to England shall along with you. (3.3.1-4)
The young men, who are supposedly friends of Hamlet, do not defend him, but readily agree to the commands of the king without objections. Most critics few these two courtiers as opportunists who seek favor and position from the king. So, they are in collusion with Claudius by not objecting to spy on their friend, and they also seek to rise in political power in their acts of compliance with the king.
Of course, the sycophantic Polonius is more than willing to spy upon Hamlet, and to even have his daughter be complicit in this spying. Moreover, he himself is the initiator of the surveillance. For, it is he who approaches Gertrude with the news that her son is mad and should be observed. In Act II, Scene 2, he further informs Gertrude that Hamlet has written Ophelia a letter, part of which is offensive. Claudius senses easily Polonius's motives, but pretends that he thinks him "...a man faithful and honorable" (2.2.129).
Clearly, the greatest power that Claudius wields is his position as king per se, the highest ruler of Denmark. For, he can grant favors, elevate others to social and political positions that exceed their current ones, and he also has the power to destroy him if they disagree with his actions. While his orders for surveillance of Hamlet demand compliance because of this puissance, they also offer political advancement for such opportunists as Rosencrantz and Guildenstern and Polonius.